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Convex comparison of Gaussian mixtures 高斯混合的凸比较
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-05-07 DOI: 10.1016/j.jmva.2025.105448
Benjamin Jourdain , Gilles Pagès
{"title":"Convex comparison of Gaussian mixtures","authors":"Benjamin Jourdain ,&nbsp;Gilles Pagès","doi":"10.1016/j.jmva.2025.105448","DOIUrl":"10.1016/j.jmva.2025.105448","url":null,"abstract":"<div><div>Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105448"},"PeriodicalIF":1.4,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A non-parametric U-statistic testing approach for multi-arm clinical trials with multivariate longitudinal data 多臂临床试验多变量纵向数据的非参数u统计检验方法
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-05-02 DOI: 10.1016/j.jmva.2025.105447
Dhrubajyoti Ghosh, Sheng Luo
{"title":"A non-parametric U-statistic testing approach for multi-arm clinical trials with multivariate longitudinal data","authors":"Dhrubajyoti Ghosh,&nbsp;Sheng Luo","doi":"10.1016/j.jmva.2025.105447","DOIUrl":"10.1016/j.jmva.2025.105447","url":null,"abstract":"<div><div>Randomized clinical trials (RCTs) often involve multiple longitudinal primary outcomes to comprehensively assess treatment efficacy. The Longitudinal Rank-Sum Test (LRST) Xu et al. (2025), a robust U-statistics-based, non-parametric, rank-based method, effectively controls Type I error and enhances statistical power by leveraging the temporal structure of the data without relying on distributional assumptions. However, the LRST is limited to two-arm comparisons. To address the need for comparing multiple doses against a control group in many RCTs, we extend the LRST to a multi-arm setting. This novel multi-arm LRST provides a flexible and powerful approach for evaluating treatment efficacy across multiple arms and outcomes, with a strong capability for detecting the most effective dose in multi-arm trials. Extensive simulations demonstrate that this method maintains excellent Type I error control while providing greater power compared to the two-arm LRST with multiplicity adjustments. Application to the Bapineuzumab (Bapi) 301 trial further validates the multi-arm LRST’s practical utility and robustness, confirming its efficacy in complex clinical trial analyses.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105447"},"PeriodicalIF":1.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Consistency for constrained maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions under general data generating processes 基于椭圆对称分布混合的约束最大似然估计和聚类在一般数据生成过程中的一致性
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-04-25 DOI: 10.1016/j.jmva.2025.105446
Pietro Coretto , Christian Hennig
{"title":"Consistency for constrained maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions under general data generating processes","authors":"Pietro Coretto ,&nbsp;Christian Hennig","doi":"10.1016/j.jmva.2025.105446","DOIUrl":"10.1016/j.jmva.2025.105446","url":null,"abstract":"<div><div>The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution <span><math><mi>P</mi></math></span> is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where <span><math><mi>P</mi></math></span> is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of <span><math><mi>P</mi></math></span>. This provides some theoretical justification for the use of such estimators for cluster analysis in case that <span><math><mi>P</mi></math></span> has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105446"},"PeriodicalIF":1.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process 双参数弱平稳随机过程的倏逝部分的算子理论方法
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-04-15 DOI: 10.1016/j.jmva.2025.105445
Zbigniew Burdak , Marek Kosiek , Patryk Pagacz , Marek Słociński
{"title":"An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process","authors":"Zbigniew Burdak ,&nbsp;Marek Kosiek ,&nbsp;Patryk Pagacz ,&nbsp;Marek Słociński","doi":"10.1016/j.jmva.2025.105445","DOIUrl":"10.1016/j.jmva.2025.105445","url":null,"abstract":"<div><div>A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceeded. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper, we describe the most untouchable one — the evanescent part. Moreover, we point out how this part depends on the shape of the past.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105445"},"PeriodicalIF":1.4,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hoeffding decomposition of functions of random dependent variables 随机因变量函数的Hoeffding分解
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-04-02 DOI: 10.1016/j.jmva.2025.105444
Marouane Il Idrissi , Nicolas Bousquet , Fabrice Gamboa , Bertrand Iooss , Jean-Michel Loubes
{"title":"Hoeffding decomposition of functions of random dependent variables","authors":"Marouane Il Idrissi ,&nbsp;Nicolas Bousquet ,&nbsp;Fabrice Gamboa ,&nbsp;Bertrand Iooss ,&nbsp;Jean-Michel Loubes","doi":"10.1016/j.jmva.2025.105444","DOIUrl":"10.1016/j.jmva.2025.105444","url":null,"abstract":"<div><div>Hoeffding’s functional decomposition is the cornerstone of many post-hoc interpretability methods. It entails decomposing arbitrary functions of mutually independent random variables as a sum of interactions. Many generalizations to dependent covariables have been proposed throughout the years, which rely on finding a set of suitable projectors. This paper characterizes such projectors under hierarchical orthogonality constraints and mild assumptions on the variable’s probabilistic structure. Our approach is deeply rooted in Hilbert space theory, giving intuitive insights on defining, identifying, and separating interactions from the effects due to the variables’ dependence structure. This new decomposition is then leveraged to define a new functional analysis of variance. Toy cases of functions of bivariate Bernoulli and Gaussian random variables are studied.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105444"},"PeriodicalIF":1.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotics of estimators for structured covariance matrices 结构化协方差矩阵估计量的渐近性
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-03-24 DOI: 10.1016/j.jmva.2025.105443
Hendrik Paul Lopuhaä
{"title":"Asymptotics of estimators for structured covariance matrices","authors":"Hendrik Paul Lopuhaä","doi":"10.1016/j.jmva.2025.105443","DOIUrl":"10.1016/j.jmva.2025.105443","url":null,"abstract":"<div><div>We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form, that for linear covariance structures appears as the variance of a scaled projection of a random matrix that is of radial type, and a similar result is obtained for the corresponding sequence of estimators for the vector of variance components. These results are illustrated by the limiting behavior of estimators for a differentiable covariance structure in a variety of multivariate statistical models. We also derive a characterization for the influence function of corresponding functionals. Furthermore, we derive the limiting distribution and influence function of scale invariant mappings of such estimators and their corresponding functionals. As a consequence, the asymptotic relative efficiency of different estimators for the shape component of a structured covariance matrix can be compared by means of a single scalar and the gross error sensitivity of the corresponding influence functions can be compared by means of a single index. Similar results are obtained for estimators of the normalized vector of variance components. We apply our results to investigate how the efficiency, gross error sensitivity, and breakdown point of S-estimators for the normalized variance components are affected simultaneously by varying their cutoff value.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105443"},"PeriodicalIF":1.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric scale mixtures of normal distributions 正态分布的几何尺度混合
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-03-14 DOI: 10.1016/j.jmva.2025.105430
Deepak Prajapati , Sobhan Shafiei , Debasis Kundu , Ahad Jamalizadeh
{"title":"Geometric scale mixtures of normal distributions","authors":"Deepak Prajapati ,&nbsp;Sobhan Shafiei ,&nbsp;Debasis Kundu ,&nbsp;Ahad Jamalizadeh","doi":"10.1016/j.jmva.2025.105430","DOIUrl":"10.1016/j.jmva.2025.105430","url":null,"abstract":"<div><div>Recently, Kundu (2017) proposed a multivariate skewed distribution, termed the Geometric-Normal (GN) distribution, by compounding the multivariate normal distribution with the geometric distribution. This distribution is a viable alternative to Azzalini’s multivariate skew-normal distribution and possesses several desirable properties. This paper introduces a novel class of asymmetric distributions by compounding the geometric distribution with scale mixtures of normal distributions. This class constitutes a special case of the continuous mixtures of multivariate normal distributions introduced by Arellano-Valle and Azzalini (2021). The proposed multivariate distributions exhibit high flexibility, featuring heavy tails, multi-modality, and the ability to model skewness. We have also derived several properties of this class and discussed specific examples to illustrate its applications. The expectation–maximization algorithm was employed to calculate the maximum likelihood estimates of the unknown parameters. Simulation experiments have been performed to show the effectiveness of the proposed algorithm. For illustrative purposes, we have provided one multivariate data set where it has been observed that there exist members in the proposed class of models that can provide better fit compared to skew-normal, skew-t, and generalized hyperbolic distribution. In another example, it was demonstrated that when data generated from a heavy-tailed skew-t distribution is contaminated with noise, the proposed distributions offer a better fit compared to the skew-t distribution.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105430"},"PeriodicalIF":1.4,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved Gaussian mean matrix estimators in high-dimensional data 高维数据中的改进型高斯均值矩阵估计器
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-03-12 DOI: 10.1016/j.jmva.2025.105424
Arash A. Foroushani, Sévérien Nkurunziza
{"title":"Improved Gaussian mean matrix estimators in high-dimensional data","authors":"Arash A. Foroushani,&nbsp;Sévérien Nkurunziza","doi":"10.1016/j.jmva.2025.105424","DOIUrl":"10.1016/j.jmva.2025.105424","url":null,"abstract":"<div><div>In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance–covariance matrix. In particular, the main results of Chételat and Wells (2012) are established in their full generalities and we provide the corrected version of their Theorem 2. Specifically, we generalize the existing results in three ways. First, we consider a parametric estimation problem which encloses as a special case the one about the vector parameter. Second, we propose a class of James–Stein matrix estimators and, we establish a necessary and a sufficient condition for any member of the proposed class to have a finite risk function. Third, we present the conditions for the proposed class of estimators to dominate the maximum likelihood estimator. On the top of these interesting contributions, the additional novelty consists in the fact that, we extend the methods suitable for the vector parameter case and the derived results hold in the classical case as well as in the context of high and ultra-high dimensional data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105424"},"PeriodicalIF":1.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximum spacing estimation for multivariate observations under a general class of information-type measures 一类信息测度下多变量观测值的最大间距估计
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-03-06 DOI: 10.1016/j.jmva.2025.105433
Kristi Kuljus , Han Bao , Bo Ranneby
{"title":"Maximum spacing estimation for multivariate observations under a general class of information-type measures","authors":"Kristi Kuljus ,&nbsp;Han Bao ,&nbsp;Bo Ranneby","doi":"10.1016/j.jmva.2025.105433","DOIUrl":"10.1016/j.jmva.2025.105433","url":null,"abstract":"<div><div>This article considers the maximum spacing (MSP) method for multivariate observations, nearest neighbour balls are used as a multidimensional analogue to univariate spacings. Compared to the previous studies, a broader class of MSP estimators corresponding to different information-type measures is studied. The studied class of estimators includes also the estimator corresponding to the Kullback–Leibler information measure obtained with the logarithmic function. Consistency of the MSP estimators is proved when the assigned model class is correct, that is the true density belongs to the assigned class. The behaviour of the MSP estimator under different divergence measures is studied and the advantage of using MSP estimators corresponding to different information measures in the context of model validation is illustrated in simulation examples.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105433"},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143631729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimaxity under the half-Cauchy prior 半柯西先验下的极小性
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jmva.2025.105431
Yuzo Maruyama , Takeru Matsuda
{"title":"Minimaxity under the half-Cauchy prior","authors":"Yuzo Maruyama ,&nbsp;Takeru Matsuda","doi":"10.1016/j.jmva.2025.105431","DOIUrl":"10.1016/j.jmva.2025.105431","url":null,"abstract":"<div><div>This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a <span><math><mi>p</mi></math></span>-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetic.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105431"},"PeriodicalIF":1.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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