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Variable selection and debiased estimation for single ‐index expectile model
This article develops a penalised asymmetric least squares estimator for single-index expectile model. The oracle property of the proposed estimator is established. Moreover, the debiasing technique is used to construct an estimator that is asymptotically normal, which enables the construction of valid confidence intervals and hypothesis testing. Simulation studies and one real data application are conducted to illustrate the finite sample performance of the proposed methods. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - February 2, 2022 Category: Statistics Authors: Rong Jiang, Yexun Peng, Yufei Deng Tags: Original Article Source Type: research

Efficient estimation of partially linear tail index models using B ‐splines
SummaryThe tail index is an important parameter in extreme value theory. In this paper, we consider a simple yet flexible spline estimation method for partially linear tail index models. We approximate the unknown function by B-splines and construct an approximate log-likelihood function to estimate the coefficients of the linear covariates and the B-spline basis functions. Consistency and asymptotic normality of the estimators are established. Subsequently, the proposed method is illustrated by using simulations and applications to the Fremantle annual maximum sea levels data and Chicago air pollution data. (Source: Austr...
Source: Australian and New Zealand Journal of Statistics - February 2, 2022 Category: Statistics Authors: Yaolan Ma, Bo Wei Tags: Original Article Source Type: research

Properties of the affine ‐invariant ensemble sampler's ‘stretch move’ in high dimensions
We present theoretical and practical properties of the affine-invariant ensemble sampler Markov Chain Monte Carlo method. In high dimensions, the sampler's ‘stretch move’ has unusual and undesirable properties. We demonstrate this with ann-dimensional correlated Gaussian toy problem with a known mean and covariance structure, and a multivariate version of the Rosenbrock problem. Visual inspection of a trace plots suggests the burn-in period is short. Upon closer inspection, we discover the mean and the variance of the target distribution do not match the known values, and the chain takes a very long time to converge. T...
Source: Australian and New Zealand Journal of Statistics - February 2, 2022 Category: Statistics Authors: David Huijser, Jesse Goodman, Brendon J. Brewer Tags: Original Article Source Type: research

Global implicit function theorems and the online expectation –maximisation algorithm
SummaryThe expectation –maximisation (EM) algorithm framework is an important tool for statistical computation. Due to the changing nature of data, online and mini-batch variants of EM and EM-like algorithms have become increasingly popular. The consistency of the estimator sequences that are produced by these EM varian ts often rely on an assumption regarding the continuous differentiability of a parameter update function. In many cases, the parameter update function is not in closed form and may only be defined implicitly, which makes the verification of the continuous differentiability property difficult. We dem onstr...
Source: Australian and New Zealand Journal of Statistics - January 28, 2022 Category: Statistics Authors: Hien Duy Nguyen, Florence Forbes Tags: Geoff McLachlan Festschrift Source Type: research

Sufficient dimension reduction for clustered data via finite mixture modelling
SummarySufficient dimension reduction (SDR) is an attractive approach to regression modelling. However, despite its rich literature and growing popularity in application, surprisingly little research has been done on how to perform SDR for clustered data, for example as is commonly arises in longitudinal studies. Indeed, current popular SDR methods have been mostly based on a marginal estimating equation approach. In this article, we propose a new approach to SDR for clustered data based on a combination of finite mixture modelling and mixed effects regression. Finite mixture models offer a flexible means of estimating the...
Source: Australian and New Zealand Journal of Statistics - January 22, 2022 Category: Statistics Authors: F.K.C. Hui, L.H. Nghiem Tags: Geoff McLachlan Festschrift Source Type: research

Bayesian credible intervals for population attributable risk from case –control, cohort and cross‐sectional studies
SummaryPopulation attributable risk (PAR) and population attributable fraction (PAF) are used in epidemiology to predict the impact of removing a risk factor from the population. Until recently, no standard approach for calculating confidence intervals or the variance for PAR in particular was available in the literature. Previously we outlined a fully Bayesian approach to provide credible intervals for the PAR and PAF from a cross-sectional study, where the data was presented in the form of a 2 ×2 table. However, extensions to cater for other frequently used study designs were not provided. In this paper we provide metho...
Source: Australian and New Zealand Journal of Statistics - January 18, 2022 Category: Statistics Authors: Sarah Pirikahu, Geoffrey Jones, Martin L. Hazelton Tags: Original Article Source Type: research

Measuring the values of cricket players
In this study, we re solve this by measuring the value of a player in terms of how his inclusion in the team affects the team's probability of winning. With this notion of value, we develop a technique to measure the worth of a cricket player for his franchise. To illustrate this technique, we evaluate the values of cri cket players who play in the Indian Premier League. We also study the relationship between players’ values and their salaries. We find that a few popular players earn disproportionately more than others. This disproportionality in the income of popular players cannot be justified by their performa nce alo...
Source: Australian and New Zealand Journal of Statistics - January 16, 2022 Category: Statistics Authors: Pranjal Chandrakar, Shubhabrata Das Tags: Original Article Source Type: research

Detection boundary for a sparse gamma scale mixture model
SummaryWe derive the detection boundary for the one-sided version of the gamma scale mixture model where the contaminating component has a larger mean than the known reference distribution. We also derive an adaptive test which is able to almost uniformly attain the best possible performance in terms of detection of local alternatives. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - January 15, 2022 Category: Statistics Authors: Michael I. Stewart Tags: Original Article Source Type: research

Odds ?symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables
This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for alli<j, that an observation will fall in row categoryi or below, and column categoryj or above, instead of row categoryj or above, and column categoryi or below, depend on only row categoryi or column categoryj. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse ...
Source: Australian and New Zealand Journal of Statistics - January 11, 2022 Category: Statistics Authors: Shuji Ando Tags: Original Article Source Type: research

Odds ‐symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables
This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for alli<j, that an observation will fall in row categoryi or below, and column categoryj or above, instead of row categoryj or above, and column categoryi or below, depend on only row categoryi or column categoryj. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse ...
Source: Australian and New Zealand Journal of Statistics - December 7, 2021 Category: Statistics Authors: Shuji Ando Tags: Original Article Source Type: research

The Inverse G ?Wishart distribution and variational message passing
SummaryMessage passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily large graphical models. The notion of a factor graph fragment allows for compartmentalisation of algebra and computer code. We show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning. (Source: Au...
Source: Australian and New Zealand Journal of Statistics - November 28, 2021 Category: Statistics Authors: Luca Maestrini, Matt P. Wand Tags: Original Article Source Type: research

Accelerating adaptation in the adaptive Metropolis Hastings random walk algorithm
SummaryThe Metropolis Hastings random walk algorithm remains popular with practitioners due to the wide variety of situations in which it can be successfully applied and the extreme ease with which it can be implemented. Adaptive versions of the algorithm use information from the early iterations of the Markov chain t o improve the efficiency of the proposal. The aim of this paper is to reduce the number of iterations needed to adapt the proposal to the target, which is particularly important when the likelihood is time-consuming to evaluate. First, the accelerated shaping algorithm is a generalisation of both th e adapti...
Source: Australian and New Zealand Journal of Statistics - November 28, 2021 Category: Statistics Authors: Simon E.F. Spencer Tags: Original Article Source Type: research

Issue Information
(Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - November 28, 2021 Category: Statistics Tags: Issue Information Source Type: research

Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data
SummaryOutcomes in the form of rates, fractions, proportions and percentages often appear in various fields. Existing beta and simplex distributions are frequently unable to exhibit satisfactory performances in fitting such continuous data. This paper aims to develop the normalised inverse Gaussian (N-IG) distribution proposed by Lijoi, Mena& Pr ünster (2005, Journal of the American Statistical Association,100, 1278 –1291) as a new tool for analysing continuous proportional data in (0,1) and renames the N-IG as proportional inverse Gaussian (PIG) distribution. Our main contributions include: (i) To overcome the difficul...
Source: Australian and New Zealand Journal of Statistics - November 24, 2021 Category: Statistics Authors: Pengyi Liu, Guo ‐Liang Tian, Kam Chuen Yuen, Chi Zhang, Man‐Lai Tang Tags: Original Article Source Type: research

BNPdensity: Bayesian nonparametric mixture modelling in R
SummaryRobust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of para...
Source: Australian and New Zealand Journal of Statistics - November 18, 2021 Category: Statistics Authors: J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto ‐Barajas, I. Prünster Tags: Original Article Source Type: research