Journal of Multivariate Analysis最新文献

{"title":"Parametric dependence between random vectors via copula-based divergence measures","authors":"Steven De Keyser,&nbsp;Irène Gijbels","doi":"10.1016/j.jmva.2024.105336","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105336","url":null,"abstract":"<div><p>This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of <span><math><mi>Φ</mi></math></span>-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of <span><math><mi>Φ</mi></math></span>, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105336"},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141239837","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":"Tensor recovery in high-dimensional Ising models","authors":"Tianyu Liu ,&nbsp;Somabha Mukherjee ,&nbsp;Rahul Biswas","doi":"10.1016/j.jmva.2024.105335","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105335","url":null,"abstract":"<div><p>The <span><math><mi>k</mi></math></span>-tensor Ising model is a multivariate exponential family on a <span><math><mi>p</mi></math></span>-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all <span><math><mi>k</mi></math></span>-fold products of the observations, and the parameter is an unknown <span><math><mi>k</mi></math></span>-fold tensor, designed to capture higher-order interactions between the binary variables. In this paper, we describe an approach based on a penalization technique that helps us recover the signed support of the tensor parameter with high probability, assuming that no entry of the true tensor is too close to zero. The method is based on an <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-regularized node-wise logistic regression, that recovers the signed neighborhood of each node with high probability. Our analysis is carried out in the high-dimensional regime, that allows the dimension <span><math><mi>p</mi></math></span> of the Ising model, as well as the interaction factor <span><math><mi>k</mi></math></span> to potentially grow to <span><math><mi>∞</mi></math></span> with the sample size <span><math><mi>n</mi></math></span>. We show that if the minimum interaction strength is not too small, then consistent recovery of the entire signed support is possible if one takes <span><math><mrow><mi>n</mi><mo>=</mo><mi>Ω</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>!</mo><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup><msup><mrow><mi>d</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>log</mo><mfenced><mrow><mfrac><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>)</mo></mrow></mrow></math></span> samples, where <span><math><mi>d</mi></math></span> denotes the maximum degree of the hypernetwork in question. Our results are validated in two simulation settings, and applied on a real neurobiological dataset consisting of multi-array electro-physiological recordings from the mouse visual cortex, to model higher-order interactions between the brain regions.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105335"},"PeriodicalIF":1.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164340","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":"Distribution-on-distribution regression with Wasserstein metric: Multivariate Gaussian case","authors":"Ryo Okano ,&nbsp;Masaaki Imaizumi","doi":"10.1016/j.jmva.2024.105334","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105334","url":null,"abstract":"<div><p>Distribution data refer to a data set in which each sample is represented as a probability distribution, a subject area that has received increasing interest in the field of statistics. Although several studies have developed distribution-to-distribution regression models for univariate variables, the multivariate scenario remains under-explored due to technical complexities. In this study, we introduce models for regression from one Gaussian distribution to another, using the Wasserstein metric. These models are constructed using the geometry of the Wasserstein space, which enables the transformation of Gaussian distributions into components of a linear matrix space. Owing to their linear regression frameworks, our models are intuitively understandable, and their implementation is simplified because of the optimal transport problem’s analytical solution between Gaussian distributions. We also explore a generalization of our models to encompass non-Gaussian scenarios. We establish the convergence rates of in-sample prediction errors for the empirical risk minimizations in our models. In comparative simulation experiments, our models demonstrate superior performance over a simpler alternative method that transforms Gaussian distributions into matrices. We present an application of our methodology using weather data for illustration purposes.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105334"},"PeriodicalIF":1.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000411/pdfft?md5=dea43975f3758fd74adfc88e822be366&pid=1-s2.0-S0047259X24000411-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141239836","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":"Sparse subspace clustering in diverse multiplex network model","authors":"Majid Noroozi ,&nbsp;Marianna Pensky","doi":"10.1016/j.jmva.2024.105333","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105333","url":null,"abstract":"<div><p>The paper considers the DIverse MultiPLEx (DIMPLE) network model, where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. To the best of our knowledge, the DIMPLE model, introduced in Pensky and Wang (2021), presents the most broad SBM-equipped binary multilayer network model on the same set of nodes and, thus, generalizes a multitude of papers that study more restrictive settings. Under the DIMPLE model, the main task is to identify the groups of layers with the same community structures since the matrices of block connection probabilities act as nuisance parameters under the DIMPLE paradigm. The main contribution of the paper is achieving the strongly consistent between-layer clustering by using Sparse Subspace Clustering (SSC), the well-developed technique in computer vision. In addition, SSC allows to handle much larger networks than spectral clustering, and is perfectly suitable for application of parallel computing. Moreover, our paper is the first one to obtain precision guarantees for SSC when it is applied to binary data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105333"},"PeriodicalIF":1.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141095842","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 the Mai–Wang stochastic decomposition for ℓp-norm symmetric survival functions on the positive orthant","authors":"Christian Genest ,&nbsp;Johanna G. Nešlehová","doi":"10.1016/j.jmva.2024.105331","DOIUrl":"10.1016/j.jmva.2024.105331","url":null,"abstract":"<div><p>Recently, Mai and Wang (2021) investigated a class of <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-norm symmetric survival functions on the positive orthant. In their paper, they claim that the generator of these functions must be <span><math><mi>d</mi></math></span>-monotone. This note explains that this is not true in general. Luckily, most of the results in Mai and Wang (2021) are not affected by this oversight.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105331"},"PeriodicalIF":1.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000381/pdfft?md5=f0a3613b1587ac23eed097d6f63a0a06&pid=1-s2.0-S0047259X24000381-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141028268","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":"Tuning-free sparse clustering via alternating hard-thresholding","authors":"Wei Dong ,&nbsp;Chen Xu ,&nbsp;Jinhan Xie ,&nbsp;Niansheng Tang","doi":"10.1016/j.jmva.2024.105330","DOIUrl":"10.1016/j.jmva.2024.105330","url":null,"abstract":"<div><p>Model-based clustering is a commonly-used technique to partition heterogeneous data into homogeneous groups. When the analysis is to be conducted with a large number of features, analysts face simultaneous challenges in model interpretability, clustering accuracy, and computational efficiency. Several Bayesian and penalization methods have been proposed to select important features for model-based clustering. However, the performance of those methods relies on a careful algorithmic tuning, which can be time-consuming for high-dimensional cases. In this paper, we propose a new sparse clustering method based on alternating hard-thresholding. The new method is conceptually simple and tuning-free. With a user-specified sparsity level, it efficiently detects a set of key features by eliminating a large number of features that are less useful for clustering. Based on the selected key features, one can readily obtain an effective clustering of the original high-dimensional data under a general sparse covariance structure. Under mild conditions, we show that the new method leads to clusters with a misclassification rate consistent to the optimal rate as if the underlying true model were used. The promising performance of the new method is supported by both simulated and real data examples.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105330"},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141050885","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":"Bayesian inference of graph-based dependencies from mixed-type data","authors":"Chiara Galimberti ,&nbsp;Stefano Peluso ,&nbsp;Federico Castelletti","doi":"10.1016/j.jmva.2024.105323","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105323","url":null,"abstract":"<div><p>Mixed data comprise measurements of different types, with both categorical and continuous variables, and can be found in various areas, such as in life science or industrial processes. Inferring conditional independencies from the data is crucial to understand how these variables relate to each other. To this end, graphical models provide an effective framework, which adopts a graph-based representation of the joint distribution to encode such dependence relations. This framework has been extensively studied in the Gaussian and categorical settings separately; on the other hand, the literature addressing this problem in presence of mixed data is still narrow. We propose a Bayesian model for the analysis of mixed data based on the notion of Conditional Gaussian (CG) distribution. Our method is based on a canonical parameterization of the CG distribution, which allows for posterior inference of parameters indexing the (marginal) distributions of continuous and categorical variables, as well as expressing the interactions between the two types of variables. We derive the limiting Gaussian distributions, centered on the correct unknown value and with vanishing variance, for the Bayesian estimators of the canonical parameters expressing continuous, discrete and mixed interactions. In addition, we implement the proposed method for structure learning purposes, namely to infer the underlying graph of conditional independencies. When compared to alternative frequentist methods, our approach shows favorable results both in a simulation setting and in real-data applications, besides allowing for a coherent uncertainty quantification around parameter estimates.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105323"},"PeriodicalIF":1.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140906825","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":"Enhanced Laplace approximation","authors":"Jeongseop Han,&nbsp;Youngjo Lee","doi":"10.1016/j.jmva.2024.105321","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105321","url":null,"abstract":"<div><p>The Laplace approximation has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators derived from the Laplace approximation are often biased for binary or temporally and/or spatially correlated data. Additionally, the corresponding Hessian matrix tends to underestimates the standard errors of these approximate maximum likelihood estimators. While higher-order approximations have been suggested, they are not applicable to complex models, such as correlated random effects models, and fail to provide consistent variance estimators. In this paper, we propose an enhanced Laplace approximation that provides the true maximum likelihood estimator and its consistent variance estimator. We study its relationship with the variational Bayes method. We also define a new restricted maximum likelihood estimator for estimating dispersion parameters and study their asymptotic properties. Enhanced Laplace approximation generally demonstrates how to obtain the true restricted maximum likelihood estimators and their variance estimators. Our numerical studies indicate that the enhanced Laplace approximation provides a satisfactory maximum likelihood estimator and restricted maximum likelihood estimator, as well as their variance estimators in the frequentist perspective. The maximum likelihood estimator and restricted maximum likelihood estimator can be also interpreted as the posterior mode and marginal posterior mode under flat priors, respectively. Furthermore, we present some comparisons with Bayesian procedures under different priors.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105321"},"PeriodicalIF":1.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140807251","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":"Multivariate unified skew-t distributions and their properties","authors":"Kesen Wang ,&nbsp;Maicon J. Karling ,&nbsp;Reinaldo B. Arellano-Valle ,&nbsp;Marc G. Genton","doi":"10.1016/j.jmva.2024.105322","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105322","url":null,"abstract":"<div><p>The unified skew-<span><math><mi>t</mi></math></span> (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not follow the original one for unified skew-normal (SUN) distributions, yet a systematic study is lacking. In this work, explicit properties of the multivariate SUT distribution are presented, such as its stochastic representations, moments, SUN-scale mixture representation, linear transformation, additivity, marginal distribution, canonical form, quadratic form, conditional distribution, change of latent dimensions, Mardia measures of multivariate skewness and kurtosis, and non-identifiability issue. These results are given in a parameterization that reduces to the original SUN distribution as a sub-model, hence facilitating the use of the SUT for applications. Several models based on the SUT distribution are provided for illustration.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105322"},"PeriodicalIF":1.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140818150","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":"Testing distributional equality for functional random variables","authors":"Bilol Banerjee","doi":"10.1016/j.jmva.2024.105318","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105318","url":null,"abstract":"<div><p>In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modeled as elements of a separable Hilbert space <span><math><mi>H</mi></math></span>. First, we present a general recipe based on linear projections to construct a measure of dissimilarity between two probability distributions on <span><math><mi>H</mi></math></span>. In particular, we consider a measure based on the energy statistic and present some of its nice theoretical properties. A plug-in estimator of this measure is used as the test statistic to construct a general two-sample test. Large sample distribution of this statistic is derived both under null and alternative hypotheses. However, since the quantiles of the limiting null distribution are analytically intractable, the test is calibrated using the permutation method. We prove the large sample consistency of the resulting permutation test under fairly general assumptions. We also study the efficiency of the proposed test by establishing a new local asymptotic normality result for functional random variables. Using that result, we derive the asymptotic distribution of the permuted test statistic and the asymptotic power of the permutation test under local contiguous alternatives. This establishes that the permutation test is statistically efficient in the Pitman sense. Extensive simulation studies are carried out and a real data set is analyzed to compare the performance of our proposed test with some state-of-the-art methods.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105318"},"PeriodicalIF":1.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825304","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}