Journal of Multivariate Analysis最新文献_第5页

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

Online stochastic Newton methods for estimating the geometric median and applications 估计几何中值的在线随机牛顿方法及其应用

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-03-19 DOI: 10.1016/j.jmva.2024.105313

Antoine Godichon-Baggioni , Wei Lu

引用次数: 0

A consistent test of equality of distributions for Hilbert-valued random elements 希尔伯特值随机元素分布相等的一致性检验

IF 1.6 3区数学

Journal of Multivariate Analysis Pub Date : 2024-03-15 DOI: 10.1016/j.jmva.2024.105312

Gil González–Rodríguez , Ana Colubi , Wenceslao González–Manteiga , Manuel Febrero–Bande

{"title":"A consistent test of equality of distributions for Hilbert-valued random elements","authors":"Gil González–Rodríguez , Ana Colubi , Wenceslao González–Manteiga , Manuel Febrero–Bande","doi":"10.1016/j.jmva.2024.105312","DOIUrl":"10.1016/j.jmva.2024.105312","url":null,"abstract":"<div><p>Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000198/pdfft?md5=6bc123f9555c6b95bcd432fc26329ddb&pid=1-s2.0-S0047259X24000198-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152986","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