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Abstract: In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product , where the are independent random variables, taking the values ±1 with equal probability and 0 with probability . [Copyright &y& Elsevier]

Most commonly used distributions on the unit hypersphere S k − 1 = { v ∈ R k : v ⊤ v = 1 } , k ≥ 2 , assume that the data are rotationally symmetric about some direction θ ∈ S k − 1 . However, there is empirical evidence that this assumption often fails to describe reality. We study in this paper a new class of skew-rotationally-symmetric distributions on S k − 1 that enjoy numerous good properties. We discuss the Fisher information structure of the model and derive efficient inferential procedures. In particular, we obtain the first semi-parametric test for rotational symmetry about a known direction. We also propose a second test for rotational symmetry, obtained through the definition of a new measure of skewness on the hypersphere. We investigate the finite-sample behavior of the new tests through a Monte Carlo simulation study. We conclude the paper with a discussion about some intriguing open questions related to our new models. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the problem of parameter estimation of a two-dimensional (2D) chirp model under the assumption that the errors are stationary. We define a periodogram-type function, which is based on the extension of the 2D periodogram function, defined for a 2D sinusoidal model, to the 2D chirp model. We put forward an alternative to the least squares estimators (LSEs), called the approximate least squares estimators (ALSEs). The proposed estimators take less time to compute and at the same time, they are asymptotically equivalent to the LSEs. Moreover the asymptotic properties of these estimators are obtained under slightly weaker assumptions than those required for the LSEs. Finally, we propose a sequential method for the estimation of the unknown parameters of a multiple component 2D chirp model. This method significantly reduces the computational difficulty involved in finding the usual LSEs and the ALSEs. To see how the proposed method works, we perform some simulation studies and analyze a data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

Based on the notions of colored and absolute excedances introduced by Bagno and Garber and their affine versions introduced by Mongelli, we compute the signed generating function of such statistics. Moreover, whenever possible, we derive a combinatorial interpretation of the coefficients of such generating functions. This paper is inspired by a paper of S. Sivasubramanian in which the author enumerates signed statistics on the group of classical permutations. [ABSTRACT FROM AUTHOR]

Orthogonal linear regression is a standard statistical method which is used to fit a line to a scatter plot of data points ( x i , y i ) in situations where both variables have errors. Until now the US American R.J. Adcock has been considered to be the first who published this method, which is based on the method of least squares. We show that Julius Weisbach, professor of mathematics and engineering at Bergakademie Freiberg in Saxony (Germany) had already published in 1840 a paper in which the method is fully described and applied to an interesting problem. We discuss the context of his discovery in order to understand the type of problems mining surveyors faced in that time and why the use of this method was found to be relevant in geodesy. Weisbach's method of solution is then explained in all detail. We show that he implicitly used the method of least squares, but presented the solution in terms of geometrical arguments adapted to the readership of the journal in which he published. [ABSTRACT FROM AUTHOR]

Abstract: The paper shows that the fourth cumulant of a finite mixture distribution might be decomposed into the mean of the components’ fourth cumulants and the fourth cumulant of the components’ means, when the mixture’s components have the same second and third cumulants. Statistical applications include robustness properties of likelihood-based testing procedures and kurtosis-based projection methods. Practical relevance of theoretical results in the paper are illustrated with two well-known data sets. [Copyright &y& Elsevier]

Abstract: High dimensional covariance estimation is an important topic in contemporary multivariate statistics and has recently received much attention in the mathematical statistics literature. The work of Bickel and Levina (2008) [2] introduces a general approach to such estimation problems in a large class of models: banding of the sample covariance matrix. Bickel and Levina show that banded estimators are consistent in the operator norm as the dimension of the covariance matrix, , and the sample size, , both go to infinity. Critically, these estimators rely on knowing the order of the covariates apriori before banding can be applied. A rigorous framework for order recovery is however not available in the literature. In this paper, we propose a novel framework and methodology that can be used to recover covariate order in general classes of banded models. Such models can also be framed as autoregressive processes, which in turn fall within the class of graphical models. We show that recovering covariate order is intimately related to minimizing functionals on the symmetric group. Indeed, an important contribution of the paper is a result showing that the natural time order in such an autoregressive process has the property that over all orderings of covariates, it minimizes the sum of the diagonals of the Cholesky decomposition, of both the covariance and the inverse covariance matrix. This result lays the foundation for the ensuing statistical methodology developed in this paper: an efficient algorithm called the Best Permutation Algorithm (BPA). The BPA can recover the natural order of variables in autoregressive models at the rate of , which is the same rate that the covariance matrix can be estimated if the natural time order were known. Hence the BPA yields the oracle rate. Moreover, the computational complexity of the BPA is proved to be polynomial in the number of variables, , and hence allows for an efficient search over the full permutation group on letters, a group whose size is super-exponential in . The methodology is also successfully illustrated on numerical examples. [Copyright &y& Elsevier]

Abstract: For many of the unsolved problems concerning cycles and matchings in graphs it is known that it is sufficient to prove them for snarks, the class of non-trivial 3-regular graphs which cannot be 3-edge coloured. In the first part of this paper we present a new algorithm for generating all non-isomorphic snarks of a given order. Our implementation of the new algorithm is 14 times faster than previous programs for generating snarks, and 29 times faster for generating weak snarks. Using this program we have generated all non-isomorphic snarks on vertices. Previously lists up to vertices have been published. In the second part of the paper we analyze the sets of generated snarks with respect to a number of properties and conjectures. We find that some of the strongest versions of the cycle double cover conjecture hold for all snarks of these orders, as does Jaegerʼs Petersen colouring conjecture, which in turn implies that Fulkersonʼs conjecture has no small counterexamples. In contrast to these positive results we also find counterexamples to eight previously published conjectures concerning cycle coverings and the general cycle structure of cubic graphs. [Copyright &y& Elsevier]

Liu et al. (2015) proposed a novel link-free procedure for testing whether two multi-index models share identical indices via the sufficient dimension reduction approach. However, their method can only be applied to data with two populations. In practice, we often deal with situations where the same variables are being measured on objects from three or more groups, and we would like to know how similar these groups are with respect to some overall features. In this paper, we propose a link-free method which could test if three or more multi-index models share the same indices. The asymptotic properties of our test statistic are developed. Numerical studies and a real data analysis are conducted to illustrate the performance of our method. [ABSTRACT FROM AUTHOR]

For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is its poor performance for small to moderate samples, i.e., decisions based on the WTS may become quite liberal. It is the aim of the present paper to improve the small-sample behavior of the WTS by means of a novel permutation procedure. In particular, it is shown that a permutation version of the WTS inherits its good large-sample properties while yielding a very accurate finite-sample control of the type-I error as shown in extensive simulations. Moreover, the new permutation method is motivated by a practical data set of a split plot design with a factorial structure on the repeated measures. [ABSTRACT FROM AUTHOR]

This paper proposes a new conditional kernel CCA (canonical correlation analysis) algorithm and exploits statistical consistency of it via modified Tikhonov regularization scheme, which is a continuous study of [11] . A new measure which characterizes consistency of learning ability is discussed based on the notion of distance between feature subspaces. The consistency analysis is conducted under the assumptions of normalized cross-covariance operators, which is mild and can be constructed by means of mean square contingency. Meantime, the relationship between this new measure and previous consistency scheme is investigated. Furthermore, we study conditional kernel CCA in a more general scenario by means of the trace operator. [ABSTRACT FROM AUTHOR]

Abstract: This paper quantifies the form of the asymptotic covariance matrix of the sample autocovariances in a multivariate stationary time series—the classic Bartlett formula. Such quantification is useful in many statistical inferences involving autocovariances. While joint asymptotic normality of the sample autocovariances is well-known in univariate settings, explicit forms of the asymptotic covariances have not been investigated in the general multivariate non-Gaussian case. We fill this gap by providing such an analysis, bookkeeping all skewness terms. Additionally, following a recent univariate paper by Francq and Zakoian, we consider linear processes driven by non-independent errors, a feature that permits consideration of multivariate GARCH processes. [Copyright &y& Elsevier]

Abstract: Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case. [Copyright &y& Elsevier]

Abstract: The BLU properties of OLS estimators under known assumptions have encouraged the widespread use of OLS multivariate regression analysis in many empirical studies that are based upon a conceptual model of a single explanatory equation. However, such a model may well be an imperfect empirical approximation to the valid underlying conceptual model, that may well contain several important additional inter-relationships between the relevant variables. In this paper, we examine the conditions under which we can predict the direction of the resultant endogeneity bias that will prevail in the OLS asymptotic parameter estimates for any given endogenous or predetermined variable, and the extent to which we can rely upon simple heuristics in this process. We also identify the underlying structural parameters to which the magnitude of the endogeneity bias is sensitive. The importance of such sensitivity analysis has been underlined by an increasing awareness of the inability of standard diagnostic tests to shed light upon the extent of the endogeneity bias, rather than upon merely its existence. The paper examines the implications of the analysis for statistical inferences about the true value of the regression coefficients and the validity of associated -statistics. [Copyright &y& Elsevier]

Abstract: The paper is about the asymptotic properties of the maximum likelihood estimator for the extreme value index. Under the second order condition, Drees et al. [H. Drees, A. Ferreira, L. de Haan, On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab. 14 (2004) 1179–1201] proved asymptotic normality for any solution of the likelihood equations (with shape parameter ) that is not too far off the real value. But they did not prove that there is a solution of the equations satisfying the restrictions. In this paper, the existence is proved, even for . The proof just uses the domain of attraction condition (first order condition), not the second order condition. It is also proved that the estimator is consistent. When the second order condition is valid, following the current proof, the existence of a solution satisfying the restrictions in the above-cited reference is a direct consequence. [Copyright &y& Elsevier]

Abstract: In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive self-complementary -uniform hypergraph of order , where or and , then the highest power of any prime dividing must be congruent to 1 modulo . We show that this necessary condition is also sufficient in many cases–for example, for a prime power, and for and odd–thus generalizing the result on vertex-transitive self-complementary graphs of Rao and Muzychuk. We also give sufficient conditions for the existence of vertex-transitive self-complementary uniform hypergraphs in several other cases. Since vertex-transitive self-complementary uniform hypergraphs are equivalent to a certain kind of large sets of -designs, the results of the paper imply the corresponding results in design theory. [Copyright &y& Elsevier]

Abstract: In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) only require that the data-generating process satisfies a certain law of large numbers. We then consider the learnability of SVMs for -mixing (not necessarily stationary) processes for both classification and regression, where for the latter we explicitly allow unbounded noise. [Copyright &y& Elsevier]

Based on data mining technology, this paper incorporates Bayesian networks to examine ecosystem data in order to investigate the static and dynamic benefits of returning farmland to forests and ecological compensation. The restricted network structure is suggested to reduce training costs and simplify model structure. Simultaneously, in order to increase prediction accuracy over a single model, ensemble learning is utilized to train multiple models to solve the same problem. Furthermore, based on data mining, this article explores the ecosystem's development purpose, constituent elements, and static framework, illustrates its operation and evolution mechanism, and constructs an evaluation system for returning farmland to forest and ecological compensation. Finally, this article incorporates current situation to determine the static and dynamic benefits, and then systematically verifies it using experiments and mathematical statistics. The research findings indicate that the impact of the framework built in this paper meets the standards of the construction model which could be used in practice. • Evaluate the static benefits and dynamic effects of returning farmland. • Analyzed ecological compensation benefits & established dynamic cycle compensation model. • Illustrates operation & evolution mechanism, and constructs an evaluation system for returning farmland. [ABSTRACT FROM AUTHOR]

Environmental policies and guidelines often specify standards for environmental indicators. The first part of this paper argues that, where compliance with these standards is assessed with the help of statistical inference, an inference employing a three-alternatives decision rule can provide more sensible feedback to environmental managers for precautionary decision-making. The second part of the paper shows how a three-alternatives statistical inference about compliance with a percentile standard might be applied to a small number of observations using a non-parametric binomial interval. This interval expression of uncertainty results in the sample size requirements for various percentile ranks becoming explicit. [Copyright &y& Elsevier]

Abstract: A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall–Olkin type. A mixture of the proposed bivariate distributions is also discussed. The results obtained here generalize those of the bivariate exponential distribution present in the literature. [Copyright &y& Elsevier]

Abstract: In risk management, ignoring the dependence among various types of claims often results in over-estimating or under-estimating the ruin probabilities of a portfolio. This paper focuses on three commonly used ruin probabilities in multivariate compound risk models, and using the comparison methods shows how some ruin probabilities increase, whereas the others decrease, as the claim dependence grows. The paper also presents some computable bounds for these ruin probabilities, which can be calculated explicitly for multivariate phase-type distributed claims, and illustrates the performance of these bounds for the multivariate compound Poisson risk models with slightly or highly dependent Marshall–Olkin exponential claim sizes. [Copyright &y& Elsevier]

Abstract: In this paper we study the stability of transonic shocks in steady supersonic flow past a wedge. We take the potential flow equation as the mathematical model to describe the compressible flow. It is known that in generic case such a problem admits two possible location of shock, connecting the flow ahead it and behind it. They can be distinguished as supersonic–supersonic shock and supersonic–subsonic shock (or transonic shock). Both these possible shocks satisfy the Rankine–Hugoniot conditions and entropy condition. In this paper we prove that the transonic shock is also stable under perturbation of the coming flow provided the pressure at infinity is well controlled. [Copyright &y& Elsevier]

Abstract: The (univariate) -distribution and symmetric V.G. distribution are competing models [D.S. Madan, E. Seneta, The variance gamma (V.G.) model for share market returns, J. Business 63 (1990) 511–524; T.W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2000 (Section 9.4)] for the distribution of log-increments of the price of a financial asset. Both result from scale-mixing of the normal distribution. The analogous matrix variate distributions and their characteristic functions are derived in the sequel and are dual to each other in the sense of a simple Duality Theorem. This theorem can thus be used to yield the derivation of the characteristic function of the t-distribution and is the essence of the idea used by Dreier and Kotz [A note on the characteristic function of the -distribution, Statist. Probab. Lett. 57 (2002) 221–224]. The present paper generalizes the univariate ideas in Section 6 of Seneta [Fitting the variance-gamma (VG) model to financial data, stochastic methods and their applications, Papers in Honour of Chris Heyde, Applied Probability Trust, Sheffield, J. Appl. Probab. (Special Volume) 41A (2004) 177–187] to the general matrix generalized inverse gaussian (MGIG) distribution. [Copyright &y& Elsevier]

Abstract: The early work of Zellner on the multivariate Student- linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter and on the regression coefficients . Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed. The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right. [Copyright &y& Elsevier]

Abstract: In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281–305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes -gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift. [Copyright &y& Elsevier]

Abstract: Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example. [Copyright &y& Elsevier]

For a subgroup T of a group G( ∘ ), letL ∘ (T) andR ∘ (T) denote the sets of all left and right cosets, respectively. This paper is concerned with finite groups G( ∘ ) andG ( * ), where the places in which the Cayley tables of the two groups differ is determined by subgroups S < H ≤ G( ∘ ), such that |H : S | = 2, in the sense that for all (α, β) ∈ L ∘ (H) × R ∘ (H) one can find (α0,β0 ) ∈ L ∘ (S) × R ∘ (S) so thatα0 ⊆ α and β0 ⊆ β , and so that x ∘ y ≠ = x * y holds for (x, y) ∈ α × β if and only if (x, y) ∈ α0 × β0. GivenG ( ∘ ) and G( * ), there can be multiple choices ofS and H and it is proved in the paper that there always exists a choice for which S is a normal subgroup of both G( ∘ ) and G( * ), andG ( ∘ ) / S = G ( * ) / S is either cyclic or dihedral (where the latter includes Klein’s four-element group). The specification of S and H is precise enough to permit a detailed description of the set of products for which ∘ and * differ and of the way in which they differ and, moreover, to permit the derivation of G( * ) fromG ( ∘ ) (without knowing G( * ) in advance). [Copyright &y& Elsevier]

We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of U -statistics, built from wavelets coefficients evaluated on a spherical Poisson field of arbitrary dimension. For this purpose, we exploit the Stein–Malliavin approach introduced in the seminal paper by Peccati, Solé, Taqqu and Utzet (2011); we focus in particular on statistical applications covering evaluation of variance in non-parametric density estimation and Sobolev tests for uniformity. [ABSTRACT FROM AUTHOR]

Estimators of partial parameters in general linear models involve some complicated operations of the submatrices in the given matrices and their generalized inverses in the models. In this case, more efforts are needed to find variety of properties hidden behind these estimators. In this paper, we use some new analytical tools in matrix theory to investigate the connections between the ordinary least-squares estimators and the best linear unbiased estimators of the whole and partial unknown parameters in general linear model with restrictions. In particular, we derive necessary and sufficient conditions for the ordinary least-squares estimators to be the best linear unbiased estimators of the whole and partial unknown parameters in the model. [ABSTRACT FROM AUTHOR]

Given a probability measure μ , on the space of strictly positive densities M μ , we construct a topological manifold on which the elements are connected by κ -exponential models in the form q = exp κ ⁡ ( u ⊖ κ K p , κ ( u ) ) p , where exp κ ⁡ ( x ) = ( 1 + κ 2 x 2 + κ x ) 1 / κ , x ⊖ κ y = x 1 + κ 2 y 2 − y 1 + κ 2 x 2 , p , q ∈ M μ , and their local representations are elements of an Orlicz space, i.e. the manifold is modeled on Orlicz spaces. Parameter k is the G. Kaniadakis parameter for κ -deformed exponentials which is strongly relevant to relativity and statistical complex models in statistical mechanics. Functional K p , κ is the deformed counterpart of the cumulant mapping and satisfies that, if κ → 0 , we obtain the usual cumulant functional of the exponential manifold; moreover in this limit case the exponential manifold constructed by Pistone and Sempi is recovered. In the context of deformed exponentials, we prove that the function ϕ κ ( ⋅ ) = cosh κ ⁡ ( ⋅ ) − 1 , where cosh κ ⁡ ( x ) is the κ -deformed hyperbolic cosine, is a Young function and generates the Orlicz space on which the κ -exponential manifold is modeled, namely L ϕ κ ( p ⋅ μ ) . This construction differs from the one made by Pistone on the paper κ-exponential models from the geometrical viewpoint , since this last one is based on divergence functionals and modeled on Lebesgue spaces L 1 / κ ( p ⋅ μ ) . The use of κ -deformed models is interesting since they generalize the exponential models and extend them to non-additive systems. [ABSTRACT FROM AUTHOR]

Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis. [ABSTRACT FROM AUTHOR]

The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the radial component has df in the Gumbel or the Weibull max-domain of attraction. We present further results for the joint asymptotic independence and the max–sum equivalence. [ABSTRACT FROM AUTHOR]

Classification arises in a wide range of applications. A variety of statistical tools have been developed for learning classification rules from data. Understanding of their relative merits and comparisons help users to choose a proper method in practice. This paper focuses on theoretical comparison of model-based classification methods in statistics with algorithmic methods in machine learning in terms of the error rate. Extending Efron’s comparison of logistic regression with linear discriminant analysis (LDA) under the normal setting, we contrast such algorithmic methods as the support vector machine (SVM) and boosting with the LDA and logistic regression and study their relative efficiencies in reducing the error rate based on the limiting behavior of the classification boundary of each method. We show that algorithmic methods are generally less effective than model-based methods in the normal setting. In particular, loss of efficiency in error rate is typically about 33% to 60% for the SVM and 50% to 80% for boosting when compared to the LDA. However, a smooth variant of the SVM is shown to be even more efficient than logistic regression. In addition to the theoretical study, we present results from numerical experiments under various settings for comparisons of finite-sample performance and robustness to mislabeling and model misspecification. [ABSTRACT FROM AUTHOR]

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the variable selection for semiparametric varying coefficient partially linear models with longitudinal data. A new variable selection procedure is proposed based on the combination of the basis function approximations and quadratic inference functions. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure by an application. [ABSTRACT FROM AUTHOR]

Abstract: The current note discusses the consistency proof for the penalized maximum likelihood estimator of a Gaussian mixture from the paper ‘Inference for multivariate normal mixtures’ by J. Chen and X. Tan. A soft spot in that proof is identified and a rigorous alternative proof based on a uniform law of iterated logarithm is given. [Copyright &y& Elsevier]

Abstract: The minimum covariance determinant (MCD) estimator of scatter is one of the most famous robust procedures for multivariate scatter. Despite the quite important research activity related to this estimator, culminating in the recent thorough asymptotic study of Cator and Lopuhaä (2010, 2012), no results have been obtained on the corresponding estimator of shape, which is the parameter of interest in many multivariate problems (including principal component analysis, canonical correlation analysis, testing for sphericity, etc.) In this paper, we therefore propose and study MCD-based inference procedures for shape, that inherit the good robustness properties of the MCD. The main emphasis is on asymptotic results, for point estimation (Bahadur representation and asymptotic normality results) as well as for hypothesis testing (asymptotic distributions under the null and under local alternatives). Influence functions of the MCD-estimators of shape are obtained as a corollary. Monte-Carlo studies illustrate our asymptotic results and assess the robustness of the proposed procedures. [Copyright &y& Elsevier]

Abstract: Scaled and Studentized statistics are encountered frequently, and they often play a decisive role in statistical inference and testing. For instance, taking the sample mean vector and the sample covariance matrix for an iid sample , some statistics for testing normality of the underlying distribution consist of the scaled residuals (the Studentized residuals or the transformed samples), . In this paper, the distribution of the random matrix the columns of which consist of the scaled residuals is derived under elliptical distributions. Also exact distributions of Studentized statistics are discussed as an application of the main result. [Copyright &y& Elsevier]

Abstract: This paper is concerned with hierarchical data having three levels. The level 1 units are nested in the level 2 units or subclusters which are themselves nested in the level 3 clusters. The model for this data is assumed to fulfill some symmetry assumptions. The level 1 units within each subcluster are exchangeable and a permutation of the subclusters belonging to the same cluster leaves the model unchanged. We are interested in measuring the dependence associated to clusters and subclusters respectively. Two exchangeable Kendall’s tau are proposed as non parametric measures of these two associations and estimators for these measures are proposed. Their asymptotic properties are then investigated under the proposed hierarchical model for the data. These statistics are then used to estimate the intra-class correlation coefficients for data drawn from elliptical hierarchical distributions. Hypothesis tests for the cluster and subcluster effects based on the proposed estimators are developed and their performances are assessed using Pitman efficiencies and a Monte Carlo study. [Copyright &y& Elsevier]

Abstract: Quintela-del-Río (2006) considered the estimation of the maximum hazard under dependence conditions and established strong convergence with rate and asymptotic normality of the estimate. The aim of this paper is to generalize this work to the case of right censored data with covariate. Via a consistently Nadaraya–Watson weighted type estimator of the conditional hazard function, we get a non-parametric estimator of its maximum value. We establish strong representation and strong uniform consistency results for our estimators. [Copyright &y& Elsevier]

Abstract: Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method. [Copyright &y& Elsevier]

Abstract: Founder of the Brussels Observatory, Adolphe Quetelet (1796–1874) is especially well known for his theory of the average man. Like the average position of a star obtained through a large quantity of observed data, the average man was, according to Quetelet, subject to fixed causal laws. Published in 1835, his book On Man: Essay of Social Physics is one of the founding works of sociology and mathematical statistics. The sources of the analogy between astronomy and social physics have been debated by historians. To shed light on this question and the conditions of application of mathematics in the 19th century, we publish for the first time a manuscript that is kept in Quetelet's papers at the Royal Academy of Belgium, and give an English translation of it. [Copyright &y& Elsevier]

Abstract: A permutation of a multiset is called Stirling permutation if as soon as and . In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the theory of -partitions. Using certain specifications we also introduce the Stirling numbers of odd type and generalizations of the central factorial numbers. [Copyright &y& Elsevier]

Abstract: Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection- model to perform frequentist’ robust analysis of sample selection. Instead of using their maximum likelihood estimates, our paper develops new Bayesian procedures for the selection- models with either continuous or binary outcomes. By exploiting the Normal mixture representation of the distribution, we can use data augmentation to impute the missing data, and use parameter expansion to sample the restricted covariance matrices. The Bayesian procedures only involve simple steps, without calculating analytical or numerical derivatives of the complicated log likelihood functions. Simulation studies show the vulnerability of the selection models with Normal errors, as well as the robustness of the selection models with errors. Interestingly, we find evidence of heavy-tailedness in three real examples analyzed by previous studies, and the conclusions about the existence of selection effect are very sensitive to the distributional assumptions of the error terms. [Copyright &y& Elsevier]

Abstract: It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are reasonable, given the substantive context of the model; and then examining the sensitivity of inferences to reasonable changes in the prior distribution and the likelihood. Here we consider functional Bregman divergence between posterior distributions for model diagnostics, which produce methods for outlier detection as well as for prior sensitivity analysis. The methodology is exemplified through a logistic regression and a circular data model. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the Bingham distribution when the dimension is large. Our approach is to use a series expansion of the distribution from which truncation points can be determined yielding particular errors. A point of comparison with the approach of Dryden (2005) is highlighted. [Copyright &y& Elsevier]

Abstract: The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference. [Copyright &y& Elsevier]

Abstract: Let be a given probability measure and the set of -equivalent strictly positive probability densities. In this paper we construct a Banach manifold on , modeled on the space where is a reference density, for the non-parametric -exponential statistical models (Tsallis’s deformed exponential), where is any real number. This family is characterized by the fact that when , then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space. The coordinate mappings of the manifold are given in terms of Csiszár’s -divergences; the tangent vectors are identified with the one-dimensional -exponential models and -deformations of the score function. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence issue of non-central Wishart distributions which is a research topic initiated by Wishart (1928), [10] and with important contributions by e.g., Lévy (1937) [7], Gindikin (1975) [4], Shanbhag (1988) [9], Peddada and Richards (1991) [8]. We present a new method involving the theory of affine Markov processes, which reveals joint necessary conditions on the shape and non-centrality parameter. While Eaton’s conjecture concerning the necessary range of the shape parameter is confirmed, we also observe that it is not sufficient anymore that it only belongs to the Gindikin ensemble, as is in the central case. [Copyright &y& Elsevier]