Journal of Multivariate Analysis最新文献

{"title":"The k-sample problem using Gini covariance for large k","authors":"M.D. Jiménez-Gamero,&nbsp;M.R. Sillero-Denamiel","doi":"10.1016/j.jmva.2025.105463","DOIUrl":"10.1016/j.jmva.2025.105463","url":null,"abstract":"<div><div>Given <span><math><mi>k</mi></math></span> populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the <span><math><mi>k</mi></math></span> populations is addressed. With this aim, an unbiased estimator of the Gini covariance is taken as test statistic. In contrast to the classical setting, where <span><math><mi>k</mi></math></span> is kept fixed and the sample size from each population increases without bound, here <span><math><mi>k</mi></math></span> is assumed to be large and the size of each sample can either remain bounded or increase with <span><math><mi>k</mi></math></span>. The asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows us to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test based on the asymptotic null distribution and the comparison with existing tests are studied via simulation. The proposal is applied to a real data set.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"210 ","pages":"Article 105463"},"PeriodicalIF":1.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144335661","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}

{"title":"Robust Bayesian graphical modeling using γ-divergence","authors":"Takahiro Onizuka ,&nbsp;Shintaro Hashimoto","doi":"10.1016/j.jmva.2025.105461","DOIUrl":"10.1016/j.jmva.2025.105461","url":null,"abstract":"<div><div>Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods such as the graphical lasso are useful to detect significant conditional independence structures. However, the estimates are affected by outliers due to the Gaussian assumption. This paper proposes a novel robust posterior distribution for inference of Gaussian graphical models using the <span><math><mi>γ</mi></math></span>-divergence which is one of the robust divergences. In particular, we focus on the Bayesian graphical lasso by assuming the Laplace-type prior for elements of the inverse covariance matrix. The proposed posterior distribution matches its maximum a posteriori estimate with the minimum <span><math><mi>γ</mi></math></span>-divergence estimate provided by the frequentist penalized method. We show that the proposed method satisfies the posterior robustness which is a kind of measure of robustness in Bayesian analysis. The property means that the information of outliers is automatically ignored in the posterior distribution as long as the outliers are extremely large. A sufficient condition for the posterior propriety of the proposed posterior distribution is also derived. Furthermore, an efficient posterior computation algorithm via the weighted Bayesian bootstrap method is proposed. The performance of the proposed method is illustrated through simulation studies and real data analysis.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105461"},"PeriodicalIF":1.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222611","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}

{"title":"Understanding asymptotic consistency and its unique advantages in large sample statistical inference","authors":"Jiangzhou Wang ,&nbsp;Binghui Liu ,&nbsp;Bing-Yi Jing ,&nbsp;Jianhua Guo","doi":"10.1016/j.jmva.2025.105462","DOIUrl":"10.1016/j.jmva.2025.105462","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The main objective of this paper is to investigate the usefulness of asymptotic consistency in large-sample statistical inference. In many statistical applications, plug-in methods are used to construct statistics, which raises the natural question of whether the asymptotic properties of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; remain unchanged when the estimator &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is replaced by its corresponding target quantity &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. We establish that if &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is asymptotically consistent for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, meaning that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;lim&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; share identical asymptotic behaviors in terms of convergence and limiting distribution. This result notably simplifies the derivation of asymptotic properties, especially when the dependency between &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is complex. Furthermore, we systematically explore the relationship between asymptotic consistency and traditional forms of consistency, such as weak and strong consistency, clarifying their distinctions through theo","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"210 ","pages":"Article 105462"},"PeriodicalIF":1.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144469908","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}

{"title":"Measuring and testing tail equivalence","authors":"Takaaki Koike ,&nbsp;Shogo Kato ,&nbsp;Toshinao Yoshiba","doi":"10.1016/j.jmva.2025.105460","DOIUrl":"10.1016/j.jmva.2025.105460","url":null,"abstract":"<div><div>We call two copulas (lower) tail equivalent if their first-order approximations in the lower tail coincide. As a special case, a copula is called tail symmetric if it is tail equivalent to the associated survival copula. We propose a novel measure and statistical test for tail equivalence. The proposed measure takes the value of zero if and only if the two copulas share a pair of tail order and tail order parameter in common. Moreover, taking the nature of these tail quantities into account, we design the proposed measure so that it takes a large value when tail orders are different, and a small value when tail orders are the same but tail order parameters are non-identical. Therefore, the measure admits attribution of the difference in two tails to that in tail orders or in tail order parameters. We derive asymptotic properties of the proposed measure, and then propose a novel statistical test for tail equivalence. The performance of the proposed test is demonstrated in a series of simulation studies and empirical analyses of financial stock returns in the periods of the global financial crisis and the COVID-19 recession. Our empirical analysis reveals non-identical tail behaviors in different pairs of stocks, different parts of tails, and the two periods of recessions.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105460"},"PeriodicalIF":1.4,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222610","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}

{"title":"Matrix variate gamma distributions with unrestricted shape parameter","authors":"Tomasz J. Kozubowski ,&nbsp;Stepan Mazur ,&nbsp;Krzysztof Podgórski","doi":"10.1016/j.jmva.2025.105457","DOIUrl":"10.1016/j.jmva.2025.105457","url":null,"abstract":"<div><div>Matrix gamma distributions are among the most important matrix-variate laws in multivariate statistical analysis, as they encompass the Wishart distributions – the sample covariance distributions under Gaussianity – and provide a natural model for random covariances in Bayesian multivariate methods. A substantial body of literature explores this class of distributions, traditionally characterized by a shape parameter restricted to the (Gindikin) set <span><math><mrow><mrow><mo>{</mo><mi>i</mi><mo>/</mo><mn>2</mn><mo>,</mo><mi>i</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mo>}</mo></mrow><mo>∪</mo><mrow><mo>(</mo><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>k</mi><mo>×</mo><mi>k</mi></mrow></math></span> is the dimension of the matrix variate. In this paper, we show that matrix-variate gamma distributions can be naturally extended to allow the entire positive half-line as the domain of the shape parameter. This extension not only unifies the well-known singular Wishart and non-singular matrix-variate gamma distributions but also introduces new singular matrix-variate distributions with shape parameters outside the Gindikin set. While permutation invariance is no longer preserved in the singular, non-Wishart case, and its scaling properties require special treatment, our unified framework leads to new representations that bypass the restrictions of the Gindikin set. We provide several elegant and convenient stochastic representations for matrix-variate gamma distributions, which are novel even in the non-singular case. Notably, we demonstrate that the lower triangular matrix in the Cholesky factorization of a gamma-distributed matrix – whether singular or not – follows a triangular matrix-variate Rayleigh distribution, introducing a new class of matrix-valued variables that extends the classical univariate Rayleigh distribution to the matrix domain. We also briefly address statistical issues and potential applications to non-elliptical multivariate heavy tailed data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105457"},"PeriodicalIF":1.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254746","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}

{"title":"High-dimensional data analysis: Change point detection via bootstrap MOSUM","authors":"Houlin Zhou,&nbsp;Hanbing Zhu,&nbsp;Xuejun Wang","doi":"10.1016/j.jmva.2025.105449","DOIUrl":"10.1016/j.jmva.2025.105449","url":null,"abstract":"<div><div>Change point detection in high-dimensional data has become a significant area of research in the era of big data. In this paper, we propose a novel test statistic for high-dimensional change point detection based on the bootstrap moving sum (MOSUM) method. We derive the theoretical properties of the proposed statistic and establish the consistency of the change point location estimator. Numerical simulation results demonstrate that our method outperforms the bootstrap cumulative sum (CUSUM) test statistic. Finally, we apply the proposed method to empirically analyze a real-world data set.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"209 ","pages":"Article 105449"},"PeriodicalIF":1.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144231849","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}

{"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}

{"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}

{"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}

{"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}