**Geometric ergodicity for some space–time max-stable Markov chains**

Publication date: Available online 20 July 2018Source: Statistics & Probability LettersAuthor(s): Erwan Koch, Christian Y. RobertAbstractMax-stable processes are central models for spatial extremes. In this paper, we focus on some space–time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of continuous functions from the unit sphere of R3 to (0,∞). We show that these Markov chains are geometrically ergodic. An interesting feature lies in the fact that the state space is not locally compact, making the classi...

**Source: **Statistics and Probability Letters - July 20, 2018 **Category: **Statistics **Source Type: **research

**Semi-functional partial linear quantile regression**

Publication date: Available online 19 July 2018Source: Statistics & Probability LettersAuthor(s): Hui Ding, Zhiping Lu, Jian Zhang, Riquan ZhangAbstractSemi-functional partial linear model is a flexible model in which a scalar response is related to both functional covariate and scalar covariates. We propose a quantile estimation of this model as an alternative to the least square approach. We also extend the proposed method to kNN quantile method. Under some regular conditions, we establish the asymptotic normality of quantile estimators of regression coefficient. We also derive the rates of convergence of nonparametr...

**Source: **Statistics and Probability Letters - July 19, 2018 **Category: **Statistics **Source Type: **research

**Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes**

Publication date: Available online 19 July 2018Source: Statistics & Probability LettersAuthor(s): Holger fink, Georg schlüchtermannAbstractWe prove a general Picard–Lindelöf-type framework for stochastic differential equations driven by Mandelbrot–Van Ness fractional Lévy processes. This allows us to derive the existence of a fractional Lévy Cox–Ingersoll–Ross and Jacobi model with almost surely positive, respectively bounded, samples paths. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 19, 2018 **Category: **Statistics **Source Type: **research

**A self-equilibrium Friedman-like urn via stochastic approximation**

In this study, we propose a class of generalized Friedman urns with random entries. The class has the property of self-equilibrium. We prove the almost-sure convergence to the equilibrium point of this entire class by the method of stochastic approximation. We develop a central limit theorem for the proportion of white balls through the convergence theorem of stochastic approximation algorithms. We then apply this class of schemes to model the effect of trading on the price in the stock market under the efficient market hypothesis. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 19, 2018 **Category: **Statistics **Source Type: **research

**The inverse survival function for multivariate distributions and its application to the product moment**

Publication date: Available online 17 July 2018Source: Statistics & Probability LettersAuthor(s): Haruhiko OgasawaraAbstractThe inverse function of the joint survival function for continuous non-negative multivariate distributions is defined with or without change of variables. This inverse function gives three alternative expectation formulas for a non-negative random vector. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 18, 2018 **Category: **Statistics **Source Type: **research

**Synthetically lagged models**

Publication date: Available online 17 July 2018Source: Statistics & Probability LettersAuthor(s): Wesley S. Burr, Hwashin H. Shin, Glen TakaharaAbstractEpidemiologic studies often report health risk due to short-term air pollution exposure through examination of lagged association, expressing manifestation of population health effects over time. We develop a new approach to the problem of lagged manifestation of air pollution exposure: synthetically lagged models. This approach also generalizes to other lagged time series regression models. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 18, 2018 **Category: **Statistics **Source Type: **research

**Gradient and stability estimates of heat kernels for fractional powers of elliptic operator**

Publication date: Available online 11 July 2018Source: Statistics & Probability LettersAuthor(s): Yong Chen, Yaozhong Hu, Zhi WangAbstractGradient and stability type estimates of heat kernel associated with fractional power of a uniformly elliptic operator are obtained. Lp-operator norm of semigroups associated with fractional power of two uniformly elliptic operators are also obtained. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 12, 2018 **Category: **Statistics **Source Type: **research

**Strong modified transportation cost inequalities on k-concave probability measures with heavy tails**

Publication date: Available online 11 July 2018Source: Statistics & Probability LettersAuthor(s): Ying Ding, Xinsheng Zhang, Longxiang FangAbstractIn this paper, we study strong modified transportation cost inequalities for k-concave probability measures with heavy tails. We provide the polynomial-type concentration, dual representation, and tensorization properties for this kind of inequalities. And we provide integral sufficient conditions for k−concave measures (−1

**Source: **Statistics and Probability Letters - July 12, 2018 **Category: **Statistics **Source Type: **research

**A Note on Weak Convergence of General Halfspace Depth Trimmed Means**

Publication date: Available online 11 July 2018Source: Statistics & Probability LettersAuthor(s): Jin WangAbstractIn this note, we restudy the general halfspace depth trimmed means and establish the weak convergence of their sample versions, which extends the result of Massé (2009) for dimensions one and two to any dimension. The asymptotic distribution of the Donoho (1982) halfspace depth trimmed mean is obtained as a special case and concretized for elliptically symmetric distributions. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 12, 2018 **Category: **Statistics **Source Type: **research

**Editorial Board**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 11, 2018 **Category: **Statistics **Source Type: **research

**Generalized biodiversity assessment by Bayesian nested random effects models with spyke-and-slab priors**

Publication date: Available online 21 March 2018Source: Statistics & Probability LettersAuthor(s): Giovanna Jona Lasinio, Alessio Pollice, Elisa Anna FanoAbstractWe analyze variations in α-diversity of benthic macroinvertebrate communities in an Italian lagoon system using Bayesian hierarchical models with nested random effects. Our aim is to understand how spatial scales influence microhabitat definition. Tsallis entropy measures diversity and spike-and-slab regression selects predictors. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Copula-based segmentation of cylindrical time series**

Publication date: Available online 20 April 2018Source: Statistics & Probability LettersAuthor(s): Francesco LagonaAbstractA hidden Markov model is proposed for segmenting cylindrical time series according to a finite number of latent classes, associated with copula-based cylindrical densities. It provides a parsimonious and computationally tractable approach that integrates circular–linear correlation, multimodality and temporal auto-correlation. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Multivariate spatial meta kriging**

Publication date: Available online 4 May 2018Source: Statistics & Probability LettersAuthor(s): Rajarshi Guhaniyogi, Sudipto BanerjeeAbstractThis work extends earlier work on spatial meta kriging for the analysis of large multivariate spatial datasets as commonly encountered in environmental and climate sciences. Spatial meta-kriging partitions the data into subsets, analyzes each subset using a Bayesian spatial process model and then obtains approximate posterior inference for the entire dataset by optimally combining the individual posterior distributions from each subset. Importantly, as is often desired in spatial ...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Comment on “Sum of squares of uniform random variables” by I. Weissman**

Publication date: Available online 18 May 2018Source: Statistics & Probability LettersAuthor(s): Peter J. ForresterAbstractThe recent paper by Weissman (2017) is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersection of a centred ball and cube in Rn, published in the Problems and Solutions section of SIAM Review in 1997. Some recent applications of explicit formulas for the corresponding probabilities from these references, to problems in lattice reduction, and to the study of Lyapunov exponents of products of random matrices, are noted. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]**

We describe the asymptotic behavior of the Diaconis–Freedman chain on [0,1], using technics developed to study iterated Lipschitz functions systems with possibly place dependent probabilities. Under some general conditions on this family of probabilities and using quasi-compact linear operators technics, we obtain a necessary and sufficient condition for the uniqueness of the stationary probability measure for this chain and explore the case when it does not hold. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Using isotope composition and other node attributes to predict edges in fish trophic networks**

Publication date: Available online 6 June 2018Source: Statistics & Probability LettersAuthor(s): Vyacheslav Lyubchich, Ryan J. WoodlandAbstractStable isotope analysis becomes increasingly popular in ecological modeling. With exponential random graph models and machine learning techniques, this paper shows how predator isotope information and basic physical variables become predictors for the links in a trophic network. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A uniform L1 law of large numbers for functions of i.i.d. random variables that are translated by a consistent estimator**

Publication date: Available online 22 June 2018Source: Statistics & Probability LettersAuthor(s): Pierre Lafaye de Micheaux, Frédéric OuimetAbstractWe develop a new L1 law of large numbers where the ith summand is given by a function h(⋅) evaluated at Xi−θn, and where θn≗θn(X1,X2,…,Xn) is an estimator converging in probability to some parameter θ∈R. Under broad technical conditions, the convergence is shown to hold uniformly in the set of estimators interpolating between θ
and another consistent estimator θn⋆. Our main contribution is the tre...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**The necklace process: A generating function approach**

This article illustrates how, after deriving the corresponding bivariate probability generating function, the characterization of the asymptotic limiting distribution of the number of beads of a given color follows as a straightforward consequence within the analytic combinatorics framework. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Granger causality between vectors of time series: A puzzling property**

Publication date: Available online 4 July 2018Source: Statistics & Probability LettersAuthor(s): Umberto TriaccaAbstractLet us consider a discrete-time n-dimensional stochastic process z, with components x=(x1,…,xm1)′ and y=(y1,…,ym2)′, m1+m2=n. We want to study causality relationships between the variables in x andy. Suppose that we find that y Granger causes x. Then we would expect to be able to pick out at least one of these variables, say yj, having a causal impact on x. It turns out that, when we consider the conditioning information set defined by the past observations of x
and all the ...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**On the distribution of extended CIR model**

Publication date: Available online 4 July 2018Source: Statistics & Probability LettersAuthor(s): Qidi Peng, Henry SchellhornAbstractWe study the probability distribution of the interest rate in the extended Cox–Ingersoll–Ross model, where all the parameters are time-varying. We show that the distribution can be represented as that of a convergent series of weighted independent central and noncentral chi-square random variables. Simulation algorithms and their applications to finance have been discussed. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A moment coboundary theorem for C[0,1]-valued random fields**

Publication date: Available online 4 July 2018Source: Statistics & Probability LettersAuthor(s): Steven T. MorrowAbstractK. Schmidt (1977) proved that if a strictly stationary sequence of real-valued random variables has the property that the family of distributions of its partial sums is tight, then the sequence is a coboundary, meaning that it is equal to the successive differences of another strictly stationary sequence. The result here is a coboundary-type theorem for C[0,1]-valued random fields (not necessarily stationary) that includes moment conditions. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Functional analysis of spatial aggregation regions of Jeffrey pine beetle-attack within the Lake Tahoe Basin**

Publication date: Available online 6 July 2018Source: Statistics & Probability LettersAuthor(s): Ekaterina Smirnova, Omid Khormali, Joel M. EganAbstractWe introduce modeling approaches for quantifying the spatiotemporal location and characteristics of clusters with application to the 1993 Jeffrey pine beetle (JPB) forest epidemic attack. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Complete asymptotic expansions for the density function of t-distribution**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Chao-Ping ChenAbstractThe density function of t-distribution with n degrees of freedom is given by the following formula: fn(x)=Γ(n+12)πnΓ(n2)1+x2n−(n+1)∕2,x>0.Ding (1988) obtained the following asymptotic formula in terms of 1∕n: fn(x)=φ(x){1+x4−2x2−14n+3x8−28x6+30x4+12x2+396n2+O1n3},n→∞,which derives the known result limn→∞fn(x)=φ(x), where φ(x)=12πe−x2∕2 is the probability density function of the standard normal distribution. In this p...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Guiling Chen, Onno van Gaans, Sjoerd Verduyn LunelAbstractIn this paper, the existence, uniqueness and exponential stability of mild solution for a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps are studied. The existence and uniqueness of mild solution are studied by means of successive approximations, and the exponential stability in pth moment of mild solution is investigated by employing an appropriate impulsive-integral inequality. An example is given to illustrate our ma...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Pseudo-binomial approximation to (k1,k2)-runs**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): N.S. Upadhye, A.N. KumarAbstractThe distribution of (k1,k2)-runs is well-known (Dafnis et al., 2010), under independent and identically distributed (i.i.d.) setup of Bernoulli trials but is intractable under non i.i.d. setup. Hence, it is of interest to find a suitable approximate distribution for (k1,k2)-runs, under non i.i.d. setup, with reasonable accuracy. In this paper, pseudo-binomial approximation to (k1,k2)-runs is considered using total variation distance. The approximation results derived are of optimal order and impr...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**On unfair permutations**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): İlker Arslan, Ümit Işlak, Cihan PehlivanAbstractIn this paper we study the inverse of so-called unfair permutations. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave very much alike in case of locally dependent random variables. As an example of a globally dependent statistic we use the number of inversions, and show that this statistic satisfies a central limit theorem after proper centering and scaling. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Long time behavior for stochastic Burgers equations with jump noises**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Guanying Wang, Xingchun Wang, Ke ZhouAbstractIn this paper, we consider stochastic Burgers equations driven by compensated Poisson random measures. Under some appropriate conditions, we investigate the exponential stability on the solutions of the equations. Examples are presented to illustrate the applications of the results. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A proof for the existence of multivariate singular generalized skew-elliptical density functions**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Tomer ShushiAbstractWe derive the density functions of multivariate singular generalized skew-elliptical distributions, present their characteristic function, and derive explicit formulas for the expectation and the covariance matrix. This letter generalizes results given in Díaz-García et al. (2002) and Young et al. (2016) about the existence of multivariate singular elliptical and multivariate singular skew-normal density functions, respectively. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A note on the spectral gap for general harmonic measures on spheres**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Yutao Ma, Xinyu WangAbstractIn this paper, we consider general harmonic measures μxn,β on the unit sphere Sn−1 in Rn, where x∈Rn with 0≤|x|

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Velocity formulae between entropy and hitting time for Markov chains**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Michael C.H. ChoiAbstractIn the absence of acceleration, the velocity formula gives “distance travelled equals speed multiplied by time”. For a broad class of Markov chains such as circulant Markov chains or random walk on complete graphs, we prove a probabilistic analogue of the velocity formula between entropy and hitting time, where distance is the entropy of the Markov trajectories from state i to state j in the sense of Ekroot and Cover (1993), speed is the classical entropy rate of the chain, and the time vari...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Exact simulation of reciprocal Archimedean copulas**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Jan-Frederik MaiAbstractThe decreasing enumeration of the points of a Poisson random measure whose mean measure is Radon on (0,∞] can be represented as a non-increasing function of the jump times of a standard Poisson process. This observation allows to generalize the essential idea from a well-known exact simulation algorithm for arbitrary extreme-value copulas to copulas of more general max-infinitely divisible distributions, with reciprocal Archimedean copulas being a particular example. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Families of complementary distributions**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): M.C. JonesAbstractEach continuous distribution on (0,1), with cumulative distribution function F say, has a complementary distribution which is the distribution with cumulative distribution function F−1. Some basic general properties of complementary distributions are given.A particular focus of this article is then the construction of families of distributions, each based on a given F
and indexed by a single additional parameter, which are closed under complementarity; properties of these families of distributions are e...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Inference for partial correlation when data are missing not at random**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Tetiana Gorbach, Xavier de LunaAbstractWe introduce uncertainty regions to perform inference on partial correlations when data are missing not at random. These uncertainty regions are shown to have a desired asymptotic coverage. Their finite sample performance is illustrated via simulations and real data example. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**The semicircle law for matrices with ergodic entries**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Matthias LöweAbstractWe study the empirical spectral distribution (ESD) of symmetric random matrices with ergodic entries on the diagonals. We observe that for entries with correlations that decay to 0, when the distance of the diagonal entries becomes large the limiting ESD is the well known semicircle law. If it does not decay to 0 (and have the same sign) the semicircle law cannot be the limit of the ESD. This is in good agreement with results on exchangeable processes analyzed in Friesen and Löwe (2013) and Hochst...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Parametric estimation for non recurrent diffusion processes**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Ilham Abi-ayad, Tahar MouridAbstractWe consider the trajectory fitting estimators (TFEs) of a parameter in the drift coefficient of a non-recurrent diffusion processes introduced by Keller et al. (1984). We show the strong consistence and Gaussian limit distribution of the TFEs when one continuously observes a sample path over a time interval and obtain rate of convergence greater-order than the standard case. These results extend Dietz (2001) and Dietz and Kutoyants (2003) results in linear and polynomial cases. Numerical simu...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Dynamic optimality in optimal variance stopping problems**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): B. BuonaguidiAbstractIn an optimal variance stopping (O.V.S.) problem one seeks to determine the stopping time that maximizes the variance of an observed process. As originally shown by Pedersen (2011), the variance criterion leads to optimal stopping boundaries that depend explicitly on the initial point of the process. Then, following the lines of Pedersen and Peskir (2016), we introduce the concept of dynamic optimality for an O.V.S. problem, a type of optimality that disregards the starting point of the process. We examine ...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Some families of asymmetric nested orthogonal arrays and asymmetric sliced orthogonal arrays**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Tianfang Zhang, Junyu Jiang, Zhiming LiAbstractThis paper proposes construction algorithms for asymmetric nested and sliced orthogonal arrays with any strength. Based on group projection and algebraic techniques, families of asymmetric nested and sliced orthogonal arrays have been obtained. Examples are provided to illustrate these results. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**On some applications of Sobolev flows of SDEs with unbounded drift coefficients**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Olivier Menoukeu PamenAbstractWe study two applications of spatial Sobolev smoothness of stochastic flows of unique strong solution to stochastic differential equations (SDEs) with irregular drift coefficients. First, we analyse the stochastic transport equation assuming that the drift coefficient is Borel measurable, with spatial linear growth and show that the above equation has a unique Sobolev differentiable weak coefficient for all t∈[0,T] for T small enough. Second, we consider the Kolmogorov equation and obtain a re...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Equivalence between Mallows and Girone–Cifarelli tests**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): É. YoundjéAbstractIn this article, it is shown that the Mallows goodness-of-fit test is equivalent to the Girone–Cifarelli test. Models for which the Mallows and Girone–Cifarelli are more powerful than the Kolmogorov–Smirnov test (commonly used) are described in Friedrich and Trede (1996) and Borroni and Chiodini (2013) respectively. Our hope is that this paper will help promote the use of these appealing tests based on the L1 distance. Particularly the use of the Girone–Cifarelli test whic...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A class of space-filling designs and their projection properties**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Weiyan Mu, Shifeng XiongAbstractThis paper introduces a class of transformation-based metrics, and uses them to construct maximin-type, minimax-type, and ϕp-type designs. The proposed designs include many distance-based designs as special cases. Theoretical and numerical results are presented to show the relationship between projection properties of such a design and the transformation used in it. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A probabilistic proof for Fourier inversion formula**

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Tak Kwong Wong, Sheung Chi Phillip YamAbstractThe celebrated Fourier inversion formula provides a useful way to re-construct a regular enough, e.g. square-integrable, function via its own Fourier transform. In this article, we give the first probabilistic proof of this classical theorem, even for Euclidean spaces of arbitrary dimension. Particularly, our proof motivates why the one-half weight, for the one-dimensional case in Lemma 1, comes naturally to play due to the inherent spatial symmetry; another similar interpretation c...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Weak and one-sided strong laws for random variables with infinite mean**

Publication date: November 2018Source: Statistics & Probability Letters, Volume 142Author(s): André Adler, Anthony G. PakesAbstractLet aj be positive weight constants and Xj be independent non-negative random variables (j=1,2,…) and Sn(a)=∑i=1naiXi. If the Xj have the same relatively stable distribution, then under mild conditions there exist constants bn→∞ such that W¯n(a)=bn−1Sn(a)→p1, i.e., a weak law of large numbers holds. If the weights comprise a regularly varying sequence, then under some additional technical conditions, this outcome can be strengthened to a strong l...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Dynamic IFR concepts for coherent systems**

Publication date: November 2018Source: Statistics & Probability Letters, Volume 142Author(s): M. Burkschat, F.J. SamaniegoAbstractA conditional IFR property for a coherent system with i failed components, and a uniform IFR property, are introduced and studied. The class of mixed systems with the uniform IFR property is characterized. A pair of examples illustrate our findings. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**A proof of the transfer-current theorem in absence of reversibility**

Publication date: November 2018Source: Statistics & Probability Letters, Volume 142Author(s): L. Avena, A. GaudillièreAbstractThe transfer-current theorem is a well-known result in probability theory stating that edges in a uniform spanning tree of an undirected graph form a determinantal process with kernel interpretable in terms of flows. Its original derivation due to Burton and Pemantle (1993) is based on a clever induction using comparison of random walks with electrical networks. Several variants of this celebrated result have recently appeared in the literature. In this paper we give an elementary proof o...

**Source: **Statistics and Probability Letters - July 10, 2018 **Category: **Statistics **Source Type: **research

**Functional analysis of spatial aggregation regions of Jeffrey pine beetle-attack within the Lake Tahoe Basin**

Publication date: Available online 6 July 2018Source: Statistics & Probability LettersAuthor(s): Ekaterina Smirnova, Omid Khormali, Joel M. EganAbstractWe introduce modeling approaches for quantifying the spatiotemporal location and characteristics of clusters with application to the 1993 Jeffrey pine beetle (JPB) forest epidemic attack. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 7, 2018 **Category: **Statistics **Source Type: **research

**Generalized biodiversity assessment by Bayesian nested random effects models with spyke-and-slab priors**

Publication date: Available online 21 March 2018Source: Statistics & Probability LettersAuthor(s): Giovanna Jona Lasinio, Alessio Pollice, Elisa Anna FanoAbstractWe analyze variations in α-diversity of benthic macroinvertebrate communities in an Italian lagoon system using Bayesian hierarchical models with nested random effects. Our aim is to understand how spatial scales influence microhabitat definition. Tsallis entropy measures diversity and spike-and-slab regression selects predictors. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 5, 2018 **Category: **Statistics **Source Type: **research

**Copula-based segmentation of cylindrical time series**

Publication date: Available online 20 April 2018Source: Statistics & Probability LettersAuthor(s): Francesco LagonaAbstractA hidden Markov model is proposed for segmenting cylindrical time series according to a finite number of latent classes, associated with copula-based cylindrical densities. It provides a parsimonious and computationally tractable approach that integrates circular–linear correlation, multimodality and temporal auto-correlation. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 5, 2018 **Category: **Statistics **Source Type: **research

**Multivariate spatial meta kriging**

Publication date: Available online 4 May 2018Source: Statistics & Probability LettersAuthor(s): Rajarshi Guhaniyogi, Sudipto BanerjeeAbstractThis work extends earlier work on spatial meta kriging for the analysis of large multivariate spatial datasets as commonly encountered in environmental and climate sciences. Spatial meta-kriging partitions the data into subsets, analyzes each subset using a Bayesian spatial process model and then obtains approximate posterior inference for the entire dataset by optimally combining the individual posterior distributions from each subset. Importantly, as is often desired in spatial ...

**Source: **Statistics and Probability Letters - July 5, 2018 **Category: **Statistics **Source Type: **research

**Comment on “Sum of squares of uniform random variables” by I. Weissman**

Publication date: Available online 18 May 2018Source: Statistics & Probability LettersAuthor(s): Peter J. ForresterAbstractThe recent paper by Weissman (2017) is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersection of a centred ball and cube in Rn, published in the Problems and Solutions section of SIAM Review in 1997. Some recent applications of explicit formulas for the corresponding probabilities from these references, to problems in lattice reduction, and to the study of Lyapunov exponents of products of random matrices, are noted. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 5, 2018 **Category: **Statistics **Source Type: **research

**On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]**

We describe the asymptotic behavior of the Diaconis–Freedman chain on [0,1], using technics developed to study iterated Lipschitz functions systems with possibly place dependent probabilities. Under some general conditions on this family of probabilities and using quasi-compact linear operators technics, we obtain a necessary and sufficient condition for the uniqueness of the stationary probability measure for this chain and explore the case when it does not hold. (Source: Statistics and Probability Letters)

**Source: **Statistics and Probability Letters - July 5, 2018 **Category: **Statistics **Source Type: **research