Journal of Multivariate Analysis最新文献_第4页

Bayesian inference of graph-based dependencies from mixed-type data 从混合型数据中对基于图的依赖关系进行贝叶斯推断

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-05-06 DOI: 10.1016/j.jmva.2024.105323

Chiara Galimberti , Stefano Peluso , Federico Castelletti

{"title":"Bayesian inference of graph-based dependencies from mixed-type data","authors":"Chiara Galimberti , Stefano Peluso , 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":null,"pages":null},"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}

引用次数: 0

Enhanced Laplace approximation 增强拉普拉斯近似

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-26 DOI: 10.1016/j.jmva.2024.105321

Jeongseop Han, Youngjo Lee

{"title":"Enhanced Laplace approximation","authors":"Jeongseop Han, 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":null,"pages":null},"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}

引用次数: 0

Multivariate unified skew-t distributions and their properties 多变量统一偏斜-t 分布及其性质

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-26 DOI: 10.1016/j.jmva.2024.105322

Kesen Wang , Maicon J. Karling , Reinaldo B. Arellano-Valle , Marc G. Genton

引用次数: 0

Testing distributional equality for functional random variables 测试函数式随机变量的分布相等性

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-22 DOI: 10.1016/j.jmva.2024.105318

Bilol Banerjee

{"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":null,"pages":null},"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}

引用次数: 0

A fast and accurate kernel-based independence test with applications to high-dimensional and functional data 基于内核的快速准确独立性测试，适用于高维数据和函数数据

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-20 DOI: 10.1016/j.jmva.2024.105320

Jin-Ting Zhang , Tianming Zhu

{"title":"A fast and accurate kernel-based independence test with applications to high-dimensional and functional data","authors":"Jin-Ting Zhang , Tianming Zhu","doi":"10.1016/j.jmva.2024.105320","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105320","url":null,"abstract":"<div><p>Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent, a so-called HSIC (Hilbert–Schmidt Independence Criterion)-based test has been proposed. Its null distribution is approximated either by permutation or a Gamma approximation. In this paper, a new HSIC-based test is proposed. Its asymptotic null and alternative distributions are established. It is shown that the proposed test is root-<span><math><mi>n</mi></math></span> consistent. A three-cumulant matched chi-squared-approximation is adopted to approximate the null distribution of the test statistic. By choosing a proper reproducing kernel, the proposed test can be applied to many different types of data including multivariate, high-dimensional, and functional data. Three simulation studies and two real data applications show that in terms of level accuracy, power, and computational cost, the proposed test outperforms several existing tests for multivariate, high-dimensional, and functional data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140807250","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

Multivariate directional tail-weighted dependence measures 多变量定向尾加权依赖性测量法

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-18 DOI: 10.1016/j.jmva.2024.105319

Xiaoting Li, Harry Joe

{"title":"Multivariate directional tail-weighted dependence measures","authors":"Xiaoting Li, Harry Joe","doi":"10.1016/j.jmva.2024.105319","DOIUrl":"10.1016/j.jmva.2024.105319","url":null,"abstract":"<div><p>We propose a new family of directional dependence measures for multivariate distributions. The family of dependence measures is indexed by <span><math><mrow><mi>α</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. When <span><math><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span>, they measure the strength of dependence along different paths to the joint upper or lower orthant. For <span><math><mi>α</mi></math></span> large, they become tail-weighted dependence measures that put more weight in the joint upper or lower tails of the distribution. As <span><math><mrow><mi>α</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, we show the convergence of the directional dependence measures to the multivariate tail dependence function and characterize the convergence pattern with an asymptotic expansion. This expansion leads to a method to estimate the multivariate tail dependence function using weighted least square regression. We develop rank-based sample estimators for the tail-weighted dependence measures and establish their asymptotic distributions. The practical utility of the tail-weighted dependence measures in multivariate tail inference is further demonstrated through their application to a financial dataset.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000265/pdfft?md5=b41054186655fc814404cc641ffc0dfe&pid=1-s2.0-S0047259X24000265-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140768086","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

A uniform kernel trick for high and infinite-dimensional two-sample problems 高维和无限维二维样本问题的均匀核技巧

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-12 DOI: 10.1016/j.jmva.2024.105317

Javier Cárcamo , Antonio Cuevas , Luis-Alberto Rodríguez

{"title":"A uniform kernel trick for high and infinite-dimensional two-sample problems","authors":"Javier Cárcamo , Antonio Cuevas , Luis-Alberto Rodríguez","doi":"10.1016/j.jmva.2024.105317","DOIUrl":"10.1016/j.jmva.2024.105317","url":null,"abstract":"<div><p>We use a suitable version of the so-called ”kernel trick” to devise two-sample tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification of the practical problem of selecting an appropriate kernel function. Specifically, we apply a uniform variant of the kernel trick which involves the supremum within a class of kernel-based distances. We obtain the asymptotic distribution of the test statistic under the null and alternative hypotheses. The proofs rely on empirical processes theory, combined with the delta method and Hadamard directional differentiability techniques, and functional Karhunen–Loève-type expansions of the underlying processes. This methodology has some advantages over other standard approaches in the literature. We also give some experimental insight into the performance of our proposal compared to other kernel-based approaches (the original proposal by Borgwardt et al. (2006) and some variants based on splitting methods) as well as tests based on energy distances (Rizzo and Székely, 2017).</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000241/pdfft?md5=19f44db706891c9aa40d12d1b8b7030a&pid=1-s2.0-S0047259X24000241-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140589405","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

Sparse online regression algorithm with insensitive loss functions 损失函数不敏感的稀疏在线回归算法

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-04-03 DOI: 10.1016/j.jmva.2024.105316

Ting Hu , Jing Xiong

{"title":"Sparse online regression algorithm with insensitive loss functions","authors":"Ting Hu , Jing Xiong","doi":"10.1016/j.jmva.2024.105316","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105316","url":null,"abstract":"<div><p>Online learning is an efficient approach in machine learning and statistics, which iteratively updates models upon the observation of a sequence of training examples. A representative online learning algorithm is the online gradient descent, which has found wide applications due to its low complexity and scalability to large datasets. Kernel-based learning methods have been proven to be quite successful in dealing with nonlinearity in the data and multivariate optimization. In this paper we present a class of kernel-based online gradient descent algorithm for addressing regression problems, which generates sparse estimators in an iterative way to reduce the algorithmic complexity for training streaming datasets and model selection in large-scale learning scenarios. In the setting of support vector regression (SVR), we design the sparse online learning algorithm by introducing a sequence of insensitive distance-based loss functions. We prove consistency and error bounds quantifying the generalization performance of such algorithms under mild conditions. The theoretical results demonstrate the interplay between statistical accuracy and sparsity property during learning processes. We show that the insensitive parameter plays a crucial role in providing sparsity as well as fast convergence rates. The numerical experiments also support our theoretical results.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140533309","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

Efficient calibration of computer models with multivariate output 高效校准多变量输出的计算机模型

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-03-21 DOI: 10.1016/j.jmva.2024.105315

Yang Sun, Xiangzhong Fang

引用次数: 0

On extreme quantile region estimation under heavy-tailed elliptical distributions 重尾椭圆分布下的极值量级区域估计

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-03-20 DOI: 10.1016/j.jmva.2024.105314

Jaakko Pere , Pauliina Ilmonen , Lauri Viitasaari

引用次数: 0