Focused estimation for noisy and small data sets: a Bayesian minimum expected loss estimator approach
SummaryCentral to many inferential situations is the estimation of rational functions of parameters. The mainstream in statistics and econometrics estimates these quantities based on theplug ‐in approach without consideration of the main objective of the inferential situation. We propose the Bayesian Minimum Expected Loss (MELO) approach focusing explicitly on the function of interest, and calculating its frequentist variability. Asymptotic properties of the MELO estimator are similar to theplug ‐in approach. Nevertheless, simulation exercises show that our proposal is better in situations characterised by small sample...
Source: Australian and New Zealand Journal of Statistics - August 26, 2019 Category: Statistics Authors: Andr és Ramírez‐Hassan, Manuel Correa‐Giraldo Tags: Original Article Source Type: research

Using hidden Markov models with raw, triaxial wrist accelerometry data to determine sleep stages
SummaryAccelerometry is a low ‐cost and noninvasive method that has been used to discriminate sleep from wake, however, its utility to detect sleep stages is unclear. We detail the development and comparison of methods which utilise raw, triaxial accelerometry data to classify varying stages of sleep, ranging from sleep/wake d etection to discriminating rapid eye movement sleep, stage one sleep, stage two sleep, deep sleep and wake. First‐ and second‐order hidden Markov models (HMMs) with time‐homogeneous and time‐varying transition probability matrices, along with continuous acceleration observations in the form...
Source: Australian and New Zealand Journal of Statistics - August 24, 2019 Category: Statistics Authors: Michelle L. Trevenen, Berwin A. Turlach, Peter R. Eastwood, Leon M. Straker, Kevin Murray Tags: Original Article Source Type: research

Exact or approximate inference in graphical models: why the choice is dictated by the treewidth, and how variable elimination can be exploited
SummaryProbabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper, we review techniques exploiting the graph structure for exact inference, borrowed from optimisation and computer science. They are built on the principle of variable elimination whose complexity is dictated in an intricate way by the order in which variables are eliminated. The so ‐called treewidth of the graph characterises this algorithmic complexity: low‐treewidth gr...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: N. Peyrard, M. ‐J. Cros, S. Givry, A. Franc, S. Robin, R. Sabbadin, T. Schiex, M. Vignes Tags: Invited Review Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 61, Issue 2, Page i-iv, June 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Tags: Issue Information Source Type: research

Book Reviews
Australian&New Zealand Journal of Statistics, Volume 61, Issue 2, Page 269-270, June 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Stephanie M. Downes Tags: Book Review Source Type: research

Introduction to Bayesian Statistics, Third Edition. By William M. Bolstad and James M. Curran Hoboken, New Jersey: John Wiley and Sons. 2017. 601+xvi pages. AUD $219.95 (hardback). ISBN 9781118091562
Australian&New Zealand Journal of Statistics, Volume 61, Issue 2, Page 271-271, June 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Matthew Parry Tags: Book Review Source Type: research

Sequential imputation for models with latent variables assuming latent ignorability
SummaryModels that involve an outcome variable, covariates, and latent variables are frequently the target for estimation and inference. The presence of missing covariate or outcome data presents a challenge, particularly when missingness depends on the latent variables. This missingness mechanism is calledlatent ignorable orlatent missing at random and is a generalisation of missing at random. Several authors have previously proposed approaches for handling latent ignorable missingness, but these methods rely on prior specification of the joint distribution for the complete data. In practice, specifying the joint distribu...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Lauren J. Beesley, Jeremy M. G. Taylor, Roderick J. A. Little Tags: Original Article Source Type: research

R package rjmcmc: reversible jump MCMC using post ‐processing
SummaryTherjmcmc package forR implements the post ‐processing reversible jump Markov chain Monte Carlo (MCMC) algorithm of Barker& Link. MCMC output from each of the models is used to estimate posterior model probabilities and Bayes factors. Automatic differentiation is used to simplify implementation. The package is demonstrated on two examples. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Nicholas Gelling, Matthew R. Schofield, Richard J. Barker Tags: Original Article Source Type: research

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs
SummaryPrinciples and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure ‐balanced, not structure, but first‐order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to de pict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton‐analysis‐of‐variance tables, to as...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: C. J. Brien Tags: Original Article Source Type: research

Logistic regression analysis of non ‐randomized response data collected by the parallel model in sensitive surveys
SummaryTo study the relationship between a sensitive binary response variable and a set of non ‐sensitive covariates, this paper develops a hidden logistic regression to analyse non‐randomized response data collected via the parallel model originally proposed by Tian (2014). This is the first paper to employ the logistic regression analysis in the field of non‐randomized response techni ques. Both the Newton–Raphson algorithm and a monotone quadratic lower bound algorithm are developed to derive the maximum likelihood estimates of the parameters of interest. In particular, the proposed logistic parallel model c...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Guo ‐Liang Tian, Yin Liu, Man‐Lai Tang Tags: Original Article Source Type: research

Climate regime shift detection with a trans ‐dimensional, sequential Monte Carlo, variational Bayes method
We present an application study which exemplifies a cutting edge statistical approach for detecting climate regime shifts. The algorithm uses Bayesian computational techniques that make time ‐efficient analysis of large volumes of climate data possible. Output includes probabilistic estimates of the number and duration of regimes, the number and probability distribution of hidden states, and the probability of a regime shift in any year of the time series. Analysis of the Pacific Deca dal Oscillation (PDO) index is provided as an example. Two states are detected: one is associated with positive values of the PDO and pres...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Clare A. McGrory, Daniel C. Ahfock, Ricardo T. Lemos Tags: Original Article Source Type: research

Maximum entropy extreme ‐value seasonal adjustment
SummarySome economic series in small economies exhibit meagre (i.e. non ‐positive) values, as well as seasonal extremes. For example, agricultural variables in countries with a distinct growing season may exhibit both of these features. Multiplicative seasonal adjustment typically utilises a logarithmic transformation, but the meagre values make this impossible, while the extremes engender huge distortions that render seasonal adjustments unacceptable. To account for these features, we propose a new method of extreme‐value adjustment based on the maximum entropy principle, which results in replacement of the meagre val...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Tucker McElroy, Richard Penny Tags: Original Article Source Type: research

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs
SummaryPrinciples and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure ‐balanced, not structure, but first‐order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to de pict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton‐analysis‐of‐variance tables, to as...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: C. J. Brien Tags: Original Article Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 61, Issue 2, Page i-iv, June 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Tags: Issue Information Source Type: research

Book Reviews
Australian&New Zealand Journal of Statistics, Volume 61, Issue 2, Page 269-270, June 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Stephanie M. Downes Tags: Book Review Source Type: research

Sequential imputation for models with latent variables assuming latent ignorability
SummaryModels that involve an outcome variable, covariates, and latent variables are frequently the target for estimation and inference. The presence of missing covariate or outcome data presents a challenge, particularly when missingness depends on the latent variables. This missingness mechanism is calledlatent ignorable orlatent missing at random and is a generalisation of missing at random. Several authors have previously proposed approaches for handling latent ignorable missingness, but these methods rely on prior specification of the joint distribution for the complete data. In practice, specifying the joint distribu...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Lauren J. Beesley, Jeremy M. G. Taylor, Roderick J. A. Little Tags: Original Article Source Type: research

R package rjmcmc: reversible jump MCMC using post ‐processing
SummaryTherjmcmc package forR implements the post ‐processing reversible jump Markov chain Monte Carlo (MCMC) algorithm of Barker& Link. MCMC output from each of the models is used to estimate posterior model probabilities and Bayes factors. Automatic differentiation is used to simplify implementation. The package is demonstrated on two examples. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Nicholas Gelling, Matthew R. Schofield, Richard J. Barker Tags: Original Article Source Type: research

Climate regime shift detection with a trans ‐dimensional, sequential Monte Carlo, variational Bayes method
We present an application study which exemplifies a cutting edge statistical approach for detecting climate regime shifts. The algorithm uses Bayesian computational techniques that make time ‐efficient analysis of large volumes of climate data possible. Output includes probabilistic estimates of the number and duration of regimes, the number and probability distribution of hidden states, and the probability of a regime shift in any year of the time series. Analysis of the Pacific Deca dal Oscillation (PDO) index is provided as an example. Two states are detected: one is associated with positive values of the PDO and pres...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Clare A. McGrory, Daniel C. Ahfock, Ricardo T. Lemos Tags: Original Article Source Type: research

Maximum entropy extreme ‐value seasonal adjustment
SummarySome economic series in small economies exhibit meagre (i.e. non ‐positive) values, as well as seasonal extremes. For example, agricultural variables in countries with a distinct growing season may exhibit both of these features. Multiplicative seasonal adjustment typically utilises a logarithmic transformation, but the meagre values make this impossible, while the extremes engender huge distortions that render seasonal adjustments unacceptable. To account for these features, we propose a new method of extreme‐value adjustment based on the maximum entropy principle, which results in replacement of the meagre val...
Source: Australian and New Zealand Journal of Statistics - July 5, 2019 Category: Statistics Authors: Tucker McElroy, Richard Penny Tags: Original Article Source Type: research

Exact or approximate inference in graphical models: why the choice is dictated by the treewidth, and how variable elimination can be exploited
SummaryProbabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper, we review techniques exploiting the graph structure for exact inference, borrowed from optimisation and computer science. They are built on the principle of variable elimination whose complexity is dictated in an intricate way by the order in which variables are eliminated. The so ‐called treewidth of the graph characterises this algorithmic complexity: low‐treewidth gr...
Source: Australian and New Zealand Journal of Statistics - June 6, 2019 Category: Statistics Authors: N. Peyrard, M. ‐J. Cros, S. Givry, A. Franc, S. Robin, R. Sabbadin, T. Schiex, M. Vignes Tags: Invited Review Source Type: research

Multiphase experiments with at least one later laboratory phase. II. Non orthogonal designs
SummaryPrinciples and laws that apply to non orthogonal multiphase experiments are developed and illustrated using examples that are non orthogonal but structure ‐balanced, not structure, but first‐order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to de pict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton‐analysis‐of‐variance tables, to ...
Source: Australian and New Zealand Journal of Statistics - June 6, 2019 Category: Statistics Authors: C. J. Brien Tags: Original Article Source Type: research

Introduction to Bayesian Statistics, Third Edition. By William M. Bolstad and James M. Curran Hoboken, New Jersey: John Wiley and Sons. 2017. 601+xvi pages. AUD $219.95 (hardback). ISBN 9781118091562
Australian&New Zealand Journal of Statistics, EarlyView. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - June 6, 2019 Category: Statistics Authors: Matthew Parry Tags: Book Review Source Type: research

Logistic regression analysis of non ‐randomized response data collected by the parallel model in sensitive surveys
SummaryTo study the relationship between a sensitive binary response variable and a set of non ‐sensitive covariates, this paper develops a hidden logistic regression to analyse non‐randomized response data collected via the parallel model originally proposed by Tian (2014). This is the first paper to employ the logistic regression analysis in the field of non‐randomized response techni ques. Both the Newton–Raphson algorithm and a monotone quadratic lower bound algorithm are developed to derive the maximum likelihood estimates of the parameters of interest. In particular, the proposed logistic parallel model c...
Source: Australian and New Zealand Journal of Statistics - June 6, 2019 Category: Statistics Authors: Guo ‐Liang Tian, Yin Liu, Man‐Lai Tang Tags: Original Article Source Type: research

Posterior sampling in two classes of multivariate fractionally integrated models: corrigendum to Ravishanker, N. and B. K. Ray (1997) Australian Journal of Statistics 39 (3), 295 –311
SummaryWe discuss posterior sampling for two distinct multivariate generalisations of the univariate autoregressive integrated moving average (ARIMA) model with fractional integration. The existing approach to Bayesian estimation, introduced by Ravishanker& Ray, claims to provide a posterior ‐sampling algorithm for fractionally integrated vector autoregressive moving averages (FIVARMAs). We show that this algorithm produces posterior draws for vector autoregressive fractionally integrated moving averages (VARFIMAs), a model of independent interest that has not previously received atte ntion in the Bayesian literature...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Ross Doppelt, Keith O'Hara Tags: Corrigendum Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 61, Issue 1, Page i-iv, March 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Tags: Issue Information Source Type: research

Testing random effects in linear mixed models: another look at the F ‐test (with discussion)
This article re ‐examines the F‐test based on linear combinations of the responses, or FLC test, for testing random effects in linear mixed models. In current statistical practice, the FLC test is underused and we argue that it should be reconsidered as a valuable method for use with linear mixed models. We pre sent a new, more general derivation of the FLC test which applies to a broad class of linear mixed models where the random effects can be correlated. We highlight three advantages of the FLC test that are often overlooked in modern applications of linear mixed models, namely its computation speed, i ts generalit...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: F. K. C. Hui, Samuel M üller, A. H. Welsh Tags: Original Article Source Type: research

A note on model selection using information criteria for general linear models estimated using REML
It is common practice to compare the fit of non ‐nested models using the Akaike (AIC) or Bayesian (BIC) information criteria. The basis of these criteria is the log‐likelihood evaluated at the maximum likelihood estimates of the unknown parameters. For the general linear model (and the linear mixed model, which is a special case), estimation is usually carried out using residual or restricted maximum likelihood (REML). However, for models with different fixed effects, the residual likelihoods are not comparable and hence information criteria based on the residual likelihood cannot be used. For model selection, it is of...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Arunas Petras Verbyla Tags: Original Article Source Type: research

Confidence intervals centred on bootstrap smoothed estimators
SummaryBootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data ‐based model selection. A result of Efron in 2014 is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of this estimator. In addition, Efron considered a confidence interval centred on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard deviation. We evaluate this conf...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Paul Kabaila, Christeen Wijethunga Tags: Original Article Source Type: research

Bias correction of estimated proportions using inverse binomial group testing
SummaryGroup testing, in which individuals are pooled together and tested as a group, can be combined with inverse sampling to estimate the prevalence of a disease. Alternatives to the MLE are desirable because of its severe bias. We propose an estimator based on the bias correction method of Firth (1993), which is almost unbiased across the range of prevalences consistent with the group testing design. For equal group sizes, this estimator is shown to be equivalent to that derived by applying the correction method of Burrows (1987), and better than existing methods. For unequal group sizes, the problem has some intractabl...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Graham Hepworth Tags: Original Article Source Type: research

Constructing narrower confidence intervals by inverting adaptive tests
SummaryWe begin by describing how to find the limits of confidence intervals by using a few permutation tests of significance. Next, we demonstrate how the adaptive permutation test, which maintains its level of significance, produces confidence intervals that maintain their coverage probabilities. By inverting adaptive tests, adaptive confidence intervals can be found for any single parameter in a multiple regression model. These adaptive confidence intervals are often narrower than the traditional confidence intervals when the error distributions are long ‐tailed or skewed. We show how much reduction in width can be ac...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Thomas W. O'Gorman Tags: Original Article Source Type: research

Posterior sampling in two classes of multivariate fractionally integrated models: corrigendum to Ravishanker, N. and B. K. Ray (1997) Australian Journal of Statistics 39 (3), 295 –311
SummaryWe discuss posterior sampling for two distinct multivariate generalisations of the univariate autoregressive integrated moving average (ARIMA) model with fractional integration. The existing approach to Bayesian estimation, introduced by Ravishanker& Ray, claims to provide a posterior ‐sampling algorithm for fractionally integrated vector autoregressive moving averages (FIVARMAs). We show that this algorithm produces posterior draws for vector autoregressive fractionally integrated moving averages (VARFIMAs), a model of independent interest that has not previously received atte ntion in the Bayesian literature...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Ross Doppelt, Keith O'Hara Tags: Corrigendum Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 61, Issue 1, Page i-iv, March 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Tags: Issue Information Source Type: research

Testing random effects in linear mixed models: another look at the F ‐test (with discussion)
This article re ‐examines the F‐test based on linear combinations of the responses, or FLC test, for testing random effects in linear mixed models. In current statistical practice, the FLC test is underused and we argue that it should be reconsidered as a valuable method for use with linear mixed models. We pre sent a new, more general derivation of the FLC test which applies to a broad class of linear mixed models where the random effects can be correlated. We highlight three advantages of the FLC test that are often overlooked in modern applications of linear mixed models, namely its computation speed, i ts generalit...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: F. K. C. Hui, Samuel M üller, A. H. Welsh Tags: Original Article Source Type: research

A note on model selection using information criteria for general linear models estimated using REML
It is common practice to compare the fit of non ‐nested models using the Akaike (AIC) or Bayesian (BIC) information criteria. The basis of these criteria is the log‐likelihood evaluated at the maximum likelihood estimates of the unknown parameters. For the general linear model (and the linear mixed model, which is a special case), estimation is usually carried out using residual or restricted maximum likelihood (REML). However, for models with different fixed effects, the residual likelihoods are not comparable and hence information criteria based on the residual likelihood cannot be used. For model selection, it is of...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Arunas Petras Verbyla Tags: Original Article Source Type: research

Confidence intervals centred on bootstrap smoothed estimators
SummaryBootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data ‐based model selection. A result of Efron in 2014 is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of this estimator. In addition, Efron considered a confidence interval centred on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard deviation. We evaluate this conf...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Paul Kabaila, Christeen Wijethunga Tags: Original Article Source Type: research

Bias correction of estimated proportions using inverse binomial group testing
SummaryGroup testing, in which individuals are pooled together and tested as a group, can be combined with inverse sampling to estimate the prevalence of a disease. Alternatives to the MLE are desirable because of its severe bias. We propose an estimator based on the bias correction method of Firth (1993), which is almost unbiased across the range of prevalences consistent with the group testing design. For equal group sizes, this estimator is shown to be equivalent to that derived by applying the correction method of Burrows (1987), and better than existing methods. For unequal group sizes, the problem has some intractabl...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Graham Hepworth Tags: Original Article Source Type: research

Constructing narrower confidence intervals by inverting adaptive tests
SummaryWe begin by describing how to find the limits of confidence intervals by using a few permutation tests of significance. Next, we demonstrate how the adaptive permutation test, which maintains its level of significance, produces confidence intervals that maintain their coverage probabilities. By inverting adaptive tests, adaptive confidence intervals can be found for any single parameter in a multiple regression model. These adaptive confidence intervals are often narrower than the traditional confidence intervals when the error distributions are long ‐tailed or skewed. We show how much reduction in width can be ac...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: Thomas W. O'Gorman Tags: Original Article Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 61, Issue 1, Page i-iv, March 2019. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Tags: Issue Information Source Type: research

Testing random effects in linear mixed models: another look at the F ‐test (with discussion)
This article re ‐examines the F‐test based on linear combinations of the responses, or FLC test, for testing random effects in linear mixed models. In current statistical practice, the FLC test is underused and we argue that it should be reconsidered as a valuable method for use with linear mixed models. We pre sent a new, more general derivation of the FLC test which applies to a broad class of linear mixed models where the random effects can be correlated. We highlight three advantages of the FLC test that are often overlooked in modern applications of linear mixed models, namely its computation speed, i ts generalit...
Source: Australian and New Zealand Journal of Statistics - April 5, 2019 Category: Statistics Authors: F. K. C. Hui, Samuel M üller, A. H. Welsh Tags: Original Article Source Type: research

Bias correction of estimated proportions using inverse binomial group testing
SummaryGroup testing, in which individuals are pooled together and tested as a group, can be combined with inverse sampling to estimate the prevalence of a disease. Alternatives to the MLE are desirable because of its severe bias. We propose an estimator based on the bias correction method of Firth (1993), which is almost unbiased across the range of prevalences consistent with the group testing design. For equal group sizes, this estimator is shown to be equivalent to that derived by applying the correction method of Burrows (1987), and better than existing methods. For unequal group sizes, the problem has some intractabl...
Source: Australian and New Zealand Journal of Statistics - March 30, 2019 Category: Statistics Authors: Graham Hepworth Tags: Original Article Source Type: research

A note on model selection using information criteria for general linear models estimated using REML
It is common practice to compare the fit of non ‐nested models using the Akaike (AIC) or Bayesian (BIC) information criteria. The basis of these criteria is the log‐likelihood evaluated at the maximum likelihood estimates of the unknown parameters. For the general linear model (and the linear mixed model, which is a special case), estimation is usually carried out using residual or restricted maximum likelihood (REML). However, for models with different fixed effects, the residual likelihoods are not comparable and hence information criteria based on the residual likelihood cannot be used. For model selection, it is of...
Source: Australian and New Zealand Journal of Statistics - March 9, 2019 Category: Statistics Authors: Arunas Petras Verbyla Tags: Original Article Source Type: research

Confidence intervals centred on bootstrap smoothed estimators
SummaryBootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data ‐based model selection. A result of Efron in 2014 is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of this estimator. In addition, Efron considered a confidence interval centred on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard deviation. We evaluate this conf...
Source: Australian and New Zealand Journal of Statistics - March 5, 2019 Category: Statistics Authors: Paul Kabaila, Christeen Wijethunga Tags: Original Article Source Type: research

Posterior sampling in two classes of multivariate fractionally integrated models: corrigendum to Ravishanker, N. and B. K. Ray (1997) Australian Journal of Statistics 39 (3), 295 –311
SummaryWe discuss posterior sampling for two distinct multivariate generalisations of the univariate autoregressive integrated moving average (ARIMA) model with fractional integration. The existing approach to Bayesian estimation, introduced by Ravishanker& Ray, claims to provide a posterior ‐sampling algorithm for fractionally integrated vector autoregressive moving averages (FIVARMAs). We show that this algorithm produces posterior draws for vector autoregressive fractionally integrated moving averages (VARFIMAs), a model of independent interest that has not previously received atte ntion in the Bayesian literature...
Source: Australian and New Zealand Journal of Statistics - February 20, 2019 Category: Statistics Authors: Ross Doppelt, Keith O'Hara Tags: Erratum Source Type: research

Constructing narrower confidence intervals by inverting adaptive tests
SummaryWe begin by describing how to find the limits of confidence intervals by using a few permutation tests of significance. Next, we demonstrate how the adaptive permutation test, which maintains its level of significance, produces confidence intervals that maintain their coverage probabilities. By inverting adaptive tests, adaptive confidence intervals can be found for any single parameter in a multiple regression model. These adaptive confidence intervals are often narrower than the traditional confidence intervals when the error distributions are long ‐tailed or skewed. We show how much reduction in width can be ac...
Source: Australian and New Zealand Journal of Statistics - February 1, 2019 Category: Statistics Authors: Thomas W. O ’Gorman Tags: Original Article Source Type: research

Issue Information
Australian&New Zealand Journal of Statistics, Volume 60, Issue 4, Page i-iv, December 2018. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - December 7, 2018 Category: Statistics Tags: Issue Information Source Type: research

Using hidden Markov models to model spatial dependence in a network
This study considers spatial dependence in the number of injury crashes reported on a road network. The aggregated crash counts are considered realisations of a Poisson random variable; thus, we model both over ‐dispersion and serial correlation using the Poisson hidden Markov model (PHMM). PHMMs have typically been used for modelling temporal dependence, but they have rarely been used to model spatial dependence. Our interest, however, is specifically in relation to an underlying point process which is constrained to occur on a network. We illustrate the use of the PHMM with police‐reported data on injury road collisi...
Source: Australian and New Zealand Journal of Statistics - December 7, 2018 Category: Statistics Authors: Safaa. K. Kadhem, Paul Hewson, Irene Kaimi Tags: Original Article Source Type: research

Semiparametric model averaging prediction: a Bayesian approach
We present a novel model averaging method to construct a prediction function in semi ‐parametric form. The weighted sum of candidate semi‐parametric models is taken as a prediction of the mean response. Marginal non‐parametric regression models are approximated by spline basis functions and we apply a Bayesian Monte Carlo approach to fit such models. The optimal model weight p arameters are estimated by minimising the least squares criterion with an explicit form. We implement our method in extensive simulation studies and illustrate its use with two real medical data examples. Our methods are demonstrated to be more...
Source: Australian and New Zealand Journal of Statistics - November 27, 2018 Category: Statistics Authors: Jingli Wang, Jialiang Li Tags: Original Article Source Type: research

Variance component estimators OPE, NOPE and AOPE in linear mixed effects models
Australian&New Zealand Journal of Statistics, EarlyView. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - October 25, 2018 Category: Statistics Authors: Subir Ghosh, Li Guo, Luyao Peng Source Type: research

Data ‐adaptive test for high‐dimensional multivariate analysis of variance problem
Australian&New Zealand Journal of Statistics, EarlyView. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - September 28, 2018 Category: Statistics Authors: Mingjuan Zhang, Cheng Zhou, Yong He, Bin Liu Source Type: research

On the existence and constructions of orthogonal designs
Australian&New Zealand Journal of Statistics, EarlyView. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - September 26, 2018 Category: Statistics Authors: Ruwan C. Karunanayaka, Boxin Tang Source Type: research