Journal of Multivariate Analysis最新文献

{"title":"Graph-constrained analysis for multivariate functional data","authors":"Debangan Dey ,&nbsp;Sudipto Banerjee ,&nbsp;Martin A. Lindquist ,&nbsp;Abhirup Datta","doi":"10.1016/j.jmva.2025.105428","DOIUrl":"10.1016/j.jmva.2025.105428","url":null,"abstract":"<div><div>The manuscript considers multivariate functional data analysis with a known graphical model among the functional variables representing their conditional relationships (e.g., brain region-level fMRI data with a prespecified connectivity graph among brain regions). Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model, and cannot preserve knowledge of a given graph. We propose a method for multivariate functional analysis that exactly conforms to a given inter-variable graph. We first show the equivalence between partially separable functional GGM and graphical Gaussian processes (GP), proposed recently for constructing optimal multivariate covariance functions that retain a given graphical model. The theoretical connection helps to design a new algorithm that leverages Dempster’s covariance selection for obtaining the maximum likelihood estimate of the covariance function for multivariate functional data under graphical constraints. We also show that the finite term truncation of functional GGM basis expansion used in practice is equivalent to a low-rank graphical GP, which is known to oversmooth marginal distributions. To remedy this, we extend our algorithm to better preserve marginal distributions while respecting the graph and retaining computational scalability. The benefits of the proposed algorithms are illustrated using empirical experiments and a neuroimaging application.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105428"},"PeriodicalIF":1.4,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550673","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":"On a class of finite mixture models that includes hidden Markov models","authors":"Francesco Bartolucci ,&nbsp;Silvia Pandolfi ,&nbsp;Fulvia Pennoni","doi":"10.1016/j.jmva.2025.105423","DOIUrl":"10.1016/j.jmva.2025.105423","url":null,"abstract":"<div><div>In the context of longitudinal data, we introduce a class of finite mixture (FM) models that generalizes that of hidden Markov (HM) models, and derive conditions under which the two classes are equivalent. On the basis of this result, we develop a likelihood ratio (LR) misspecification test for assessing the latent structure of an HM model, along with a multiple version of this test that may be used in the presence of many latent states or time occasions. This testing procedure requires the maximum likelihood estimation of the two models under comparison, that is, the assumed HM model and the more general FM model, which is performed by suitable versions of the Expectation–Maximization algorithm. The approach is validated through a simulation study, aimed at assessing the performance of the proposed tests under different circumstances, and by an application using data derived from the SCImago Journal &amp; Country Rank database.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105423"},"PeriodicalIF":1.4,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445197","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}

{"title":"Statistical analysis of parsimonious high-order multivariate finite Markov chains based on sufficient statistics","authors":"Yuriy Kharin,&nbsp;Valeriy Voloshko","doi":"10.1016/j.jmva.2025.105422","DOIUrl":"10.1016/j.jmva.2025.105422","url":null,"abstract":"<div><div>A new parsimonious <span><math><mrow><mi>MCSS</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> (which stands for “Markov Chain of order <span><math><mi>s</mi></math></span> based on Sufficient Statistics”) model for multivariate discrete-valued time series is constructed. The <span><math><mrow><mi>MCSS</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> model has sufficient statistics of a simple form based on multivariate frequencies of <span><math><mrow><mo>(</mo><mi>s</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-tuples for observed time series. Special cases of the <span><math><mrow><mi>MCSS</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> model and their relations to the results known in the literature are discussed. The strong concavity property of the loglikelihood function and the uniqueness of the maximum likelihood estimator under mild regularity conditions are proven for the <span><math><mrow><mi>MCSS</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> model. Forecasting statistics for the multivariate discrete-valued time series derived with the <span><math><mrow><mi>MCSS</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> model are constructed. The developed theory is illustrated with computer experiments on simulated and real data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105422"},"PeriodicalIF":1.4,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508246","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 review of multivariate permutation tests: Findings and trends","authors":"Rosa Arboretti ,&nbsp;Elena Barzizza ,&nbsp;Nicoló Biasetton ,&nbsp;Marta Disegna","doi":"10.1016/j.jmva.2025.105421","DOIUrl":"10.1016/j.jmva.2025.105421","url":null,"abstract":"<div><div>The permutation test is a widely recognized and frequently used nonparametric hypothesis test, notable for its minimal reliance on assumptions compared to parametric tests. It has found applications in many fields, particularly in multivariate analysis. Since its introduction in the 1930s, permutation tests have been extensively examined both theoretically and empirically. This article provides the results of a comprehensive and systematic review of the literature, focusing on different aspects of multivariate permutation tests. Key articles published in international journals from 2010 onwards have been analyzed, classifying them into four main research strands: data, model, test and issues. These strands were further subdivided into more specific categories. The state of the art and significant developments in this field are summarized, followed by a discussion on future research challenges and trends, offering guidance for the design and development on new approaches.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105421"},"PeriodicalIF":1.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387240","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 of empirical distributions of sequences of graph statistics in networks with dependent edges","authors":"Jonathan R. Stewart","doi":"10.1016/j.jmva.2025.105420","DOIUrl":"10.1016/j.jmva.2025.105420","url":null,"abstract":"<div><div>One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number of realized events in the network, examples of which are degree distributions, edgewise shared partner distributions, and more. We provide conditions under which the empirical distributions of sequences of graph statistics are consistent in the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>-norm in settings where edges in the network are dependent. We accomplish this task by deriving concentration inequalities that bound probabilities of deviations of graph statistics from the expected value under weak dependence conditions. We apply our concentration inequalities to empirical distributions of sequences of graph statistics and derive non-asymptotic bounds on the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>-error which hold with high probability. Our non-asymptotic results are then extended to demonstrate uniform convergence almost surely in selected examples. We illustrate theoretical results through examples, simulation studies, and an application.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105420"},"PeriodicalIF":1.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143209494","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":"Semiparametric density estimation with localized Bregman divergence","authors":"Daisuke Matsuno ,&nbsp;Kanta Naito","doi":"10.1016/j.jmva.2025.105419","DOIUrl":"10.1016/j.jmva.2025.105419","url":null,"abstract":"<div><div>This paper examines semiparametric density estimation by combining a parametric crude guess and its nonparametric adjustment. The nonparametric adjustment is implemented via minimization of the localized Bregman divergence, which yields a broad class of semiparametric density estimators. Asymptotic theories of the density estimators in this general class are developed. Specific concrete forms of density estimators under a certain divergence and parametric guess are calculated. Simulations for several target densities and application to a real data set reveal that the proposed density estimators offer competitive or, in some cases, better performance compared to fully nonparametric kernel density estimator.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105419"},"PeriodicalIF":1.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133557","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":"Tree-structured Markov random fields with Poisson marginal distributions","authors":"Benjamin Côté,&nbsp;Hélène Cossette,&nbsp;Etienne Marceau","doi":"10.1016/j.jmva.2025.105418","DOIUrl":"10.1016/j.jmva.2025.105418","url":null,"abstract":"<div><div>A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson with the same mean, and are untied from the strength or structure of their built-in dependence. This key feature is uncommon for Markov random fields and most convenient for applications purposes. The specific properties of this new family confer a straightforward sampling procedure and analytic expressions for the joint probability mass function and the joint probability generating function of the vector of counting random variables, thus granting computational methods that scale well to vectors of high dimension. We study the distribution of the sum of random variables constituting a Markov random field from the proposed family, analyze a random variable’s individual contribution to that sum through expected allocations, and establish stochastic orderings to assess a wide understanding of their behavior.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105418"},"PeriodicalIF":1.4,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134410","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}

{"title":"New results for drift estimation in inhomogeneous stochastic differential equations","authors":"Fabienne Comte,&nbsp;Valentine Genon-Catalot","doi":"10.1016/j.jmva.2025.105415","DOIUrl":"10.1016/j.jmva.2025.105415","url":null,"abstract":"<div><div>We consider <span><math><mi>N</mi></math></span> independent and identically distributed (<em>i.i.d.</em>) stochastic processes <span><math><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>)</mo></mrow></math></span>, <span><math><mrow><mi>j</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>N</mi><mo>}</mo></mrow></mrow></math></span>, defined by a one-dimensional stochastic differential equation (SDE) with time-dependent drift and diffusion coefficient. In this context, the nonparametric estimation of a general drift function <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> from a continuous observation of the <span><math><mi>N</mi></math></span> sample paths on <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></math></span> has never been investigated. Considering a set <span><math><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>ϵ</mi></mrow></msub><mo>=</mo><mrow><mo>[</mo><mi>ϵ</mi><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><mi>A</mi></mrow></math></span>, with <span><math><mrow><mi>ϵ</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>A</mi><mo>⊂</mo><mi>R</mi></mrow></math></span>, we build by a projection method an estimator of <span><math><mi>b</mi></math></span> on <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>ϵ</mi></mrow></msub></math></span>. As the function is bivariate, this amounts to estimating a matrix of projection coefficients instead of a vector for univariate functions. We make use of Kronecker products, which simplifies the mathematical treatment of the problem. We study the risk of the estimator and distinguish the case where <span><math><mrow><mi>ϵ</mi><mo>=</mo><mn>0</mn></mrow></math></span> and the case <span><math><mrow><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>A</mi><mo>=</mo><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></mrow></math></span> compact. In the latter case, we investigate rates of convergence and prove a lower bound showing that our estimator is minimax. We propose a data-driven choice of the projection space dimension leading to an adaptive estimator. Examples of models and numerical simulation results are proposed. The method is easy to implement and works well, although computationally slower than for the estimation of a univariate function.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105415"},"PeriodicalIF":1.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562586","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":"Model averaging for global Fréchet regression","authors":"Daisuke Kurisu ,&nbsp;Taisuke Otsu","doi":"10.1016/j.jmva.2025.105416","DOIUrl":"10.1016/j.jmva.2025.105416","url":null,"abstract":"<div><div>Non-Euclidean complex data analysis becomes increasingly popular in various fields of data science. In a seminal paper, Petersen and Müller (2019) generalized the notion of regression analysis to non-Euclidean response objects. Meanwhile, in the conventional regression analysis, model averaging has a long history and is widely applied in statistics literature. This paper studies the problem of optimal prediction for non-Euclidean objects by extending the method of model averaging. In particular, we generalize the notion of model averaging for global Fréchet regressions and establish an optimal property of the cross-validation to select the averaging weights in terms of the final prediction error. A simulation study illustrates excellent out-of-sample predictions of the proposed method.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105416"},"PeriodicalIF":1.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133558","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}

{"title":"Classification using global and local Mahalanobis distances","authors":"Annesha Ghosh ,&nbsp;Anil K. Ghosh ,&nbsp;Rita SahaRay ,&nbsp;Soham Sarkar","doi":"10.1016/j.jmva.2025.105417","DOIUrl":"10.1016/j.jmva.2025.105417","url":null,"abstract":"<div><div>We propose a novel semiparametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to estimate the posterior probabilities of different classes. While popular parametric classifiers like linear and quadratic discriminant analyses are mainly motivated by the normality of the underlying distributions, the proposed classifier is more flexible and free from such parametric modeling assumptions. Since the densities of elliptic distributions are functions of Mahalanobis distances, this classifier works well when the competing classes are (nearly) elliptic. In such cases, it often outperforms popular nonparametric classifiers, especially when the sample size is small compared to the dimension of the data. To cope with non-elliptic and possibly multimodal distributions, we propose a local version of the Mahalanobis distance. Subsequently, we propose another classifier based on a generalized additive model that uses the local Mahalanobis distances as features. This nonparametric classifier usually performs like the Mahalanobis distance based semiparametric classifier when the underlying distributions are elliptic, but outperforms it for several non-elliptic and multimodal distributions. We also investigate the behavior of these two classifiers in high dimension, low sample size situations. A thorough numerical study involving several simulated and real datasets demonstrate the usefulness of the proposed classifiers in comparison to many state-of-the-art methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105417"},"PeriodicalIF":1.4,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134417","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}