Journal of Multivariate Analysis最新文献

Detection and localization of changes in a panel of densities 密度面板变化的检测和定位

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-09-24 DOI: 10.1016/j.jmva.2024.105374

{"title":"Detection and localization of changes in a panel of densities","authors":"","doi":"10.1016/j.jmva.2024.105374","DOIUrl":"10.1016/j.jmva.2024.105374","url":null,"abstract":"<div><div>We propose a new methodology for identifying and localizing changes in the Fréchet mean of a multivariate time series of probability densities. The functional data objects we study are random densities <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> indexed by discrete time <span><math><mi>t</mi></math></span> and a vector component <span><math><mi>s</mi></math></span>, which can be treated as a broadly understood spatial location. Our main objective is to identify the set of components <span><math><mi>s</mi></math></span>, where a change occurs with statistical certainty. A challenge of this analysis is that the densities <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> are not directly observable and must be estimated from sparse and potentially imbalanced data. Such setups are motivated by the analysis of two data sets that we investigate in this work. First, a hitherto unpublished large data set of Brazilian Covid infections and a second, a financial data set derived from intraday prices of U.S. Exchange Traded Funds. Chief statistical advances are the development of change point tests and estimators of components of change for multivariate time series of densities. We prove the theoretical validity of our methodology and investigate its finite sample performance in a simulation study.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327131","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

Data depth functions for non-standard data by use of formal concept analysis 利用形式概念分析实现非标准数据的数据深度函数

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-09-19 DOI: 10.1016/j.jmva.2024.105372

{"title":"Data depth functions for non-standard data by use of formal concept analysis","authors":"","doi":"10.1016/j.jmva.2024.105372","DOIUrl":"10.1016/j.jmva.2024.105372","url":null,"abstract":"<div><div>In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This covers a wide range of different data types, which we refer to as non-standard data. Depth functions have been studied intensively for normed vector spaces. However, a discussion of depth functions for non-standard data is lacking. In this article, we address this gap by using formal concept analysis to obtain a unified data representation. Building on this representation, we then define depth functions for non-standard data. Furthermore, we provide a systematic basis by introducing structural properties using the data representation provided by formal concept analysis. Finally, we embed the generalised Tukey depth into our concept of data depth and analyse it using the introduced structural properties. Thus, this article presents the mathematical formalisation of centrality and outlyingness for non-standard data and increases the number of spaces in which centrality can be discussed. In particular, we provide a basis for defining further depth functions and statistical inference methods for non-standard data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327125","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

Scaled envelope models for multivariate time series 多变量时间序列的标度包络模型

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-09-13 DOI: 10.1016/j.jmva.2024.105370

{"title":"Scaled envelope models for multivariate time series","authors":"","doi":"10.1016/j.jmva.2024.105370","DOIUrl":"10.1016/j.jmva.2024.105370","url":null,"abstract":"<div><p>Vector autoregressive (VAR) models have become a popular choice for modeling multivariate time series data due to their simplicity and ease of use. Efficient estimation of VAR coefficients is an important problem. The envelope technique for VAR models is demonstrated to have the potential to yield significant gains in efficiency and accuracy by incorporating linear combinations of the response vector that are essentially immaterial to the estimation of the VAR coefficients. However, inferences based on envelope VAR (EVAR) models are not invariant or equivariant upon the rescaling of the VAR responses, limiting their application to time series data that are measured in the same or similar units. In scenarios where VAR responses are measured on different scales, the efficiency improvements promised by envelopes are not always guaranteed. To address this limitation, we introduce the scaled envelope VAR (SEVAR) model, which preserves the efficiency-boosting capabilities of standard envelope techniques while remaining invariant to scale changes. The asymptotic characteristics of the proposed estimators are established based on different error assumptions. Simulation studies and real-data analysis are conducted to demonstrate the efficiency and effectiveness of the proposed model. The numerical results corroborate our theoretical findings.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000770/pdfft?md5=bcb10a9c98d350b55789c52bc615d145&pid=1-s2.0-S0047259X24000770-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240404","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 bias-corrected Srivastava-type test for cross-sectional independence 经偏差校正的斯里瓦斯塔瓦式横截面独立性检验

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-09-13 DOI: 10.1016/j.jmva.2024.105371

引用次数: 0

Invariant correlation under marginal transforms 边际变换下的不变相关性

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-30 DOI: 10.1016/j.jmva.2024.105361

{"title":"Invariant correlation under marginal transforms","authors":"","doi":"10.1016/j.jmva.2024.105361","DOIUrl":"10.1016/j.jmva.2024.105361","url":null,"abstract":"<div><p>A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent samples. In this paper, we study this invariance property on the Pearson correlation coefficient and its applications. A multivariate random vector is said to have an invariant correlation if its pairwise correlation coefficients remain unchanged under any common marginal transforms. For a bivariate case, we characterize all models of such a random vector via a certain combination of comonotonicity—the strongest form of positive dependence—and independence. In particular, we show that the class of exchangeable copulas with invariant correlation is precisely described by what we call positive Fréchet copulas. In the general multivariate case, we characterize the set of all invariant correlation matrices via the clique partition polytope. We also propose a positive regression dependent model that admits any prescribed invariant correlation matrix. Finally, we show that all our characterization results of invariant correlation, except one special case, remain the same if the common marginal transforms are confined to the set of increasing ones.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X2400068X/pdfft?md5=87348d6db627c38f7dec7cb4cd435464&pid=1-s2.0-S0047259X2400068X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122196","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

Grouped feature screening for ultrahigh-dimensional classification via Gini distance correlation 通过基尼距离相关性对超高维分类进行分组特征筛选

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-17 DOI: 10.1016/j.jmva.2024.105360

引用次数: 0

The inner partial least square: An exploration of the “necessary” dimension reduction 内部分最小平方：对 "必要 "降维的探索

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-14 DOI: 10.1016/j.jmva.2024.105356

引用次数: 0

Cross projection test for mean vectors via multiple random splits in high dimensions 通过高维多重随机分割对均值向量进行交叉投影测试

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-06 DOI: 10.1016/j.jmva.2024.105358

{"title":"Cross projection test for mean vectors via multiple random splits in high dimensions","authors":"","doi":"10.1016/j.jmva.2024.105358","DOIUrl":"10.1016/j.jmva.2024.105358","url":null,"abstract":"<div><p>The cross projection test (CPT) technique is extended to high-dimensional two-sample mean tests in this article, which was first proposed by Wang and Cui (2024). A data-splitting strategy is required to find the projection directions that reduce the data from high dimensional space to low dimensional space which can well solve the issue of “the curse of dimensionality”. As long as both samples are randomly split once, two correlated cross projection statistics can be established according to the CPT development mechanism, which is similar to all constructed test statistics that exist the correlation caused by multiple random splits. To deal with this issue and improve the performance of empirical powers by eliminating the randomness of data-splitting, we further utilize a powerful Cauchy combination test algorithm based on multiple data-splitting. Theoretically, we prove the asymptotic property of the proposed test statistic. Furthermore, for the sparse alternative case, we apply the power enhancement technique to the ensemble Cauchy combination test-based algorithm in marginal screening for the full data. Numerical studies through Monte Carlo simulations and two real data examples are conducted simultaneously to illustrate the utility of our proposed ensemble algorithm.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020744","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

Bayesian covariance structure modeling of interval-censored multi-way nested survival data 区间删失多向嵌套生存数据的贝叶斯协方差结构建模

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-06 DOI: 10.1016/j.jmva.2024.105359

{"title":"Bayesian covariance structure modeling of interval-censored multi-way nested survival data","authors":"","doi":"10.1016/j.jmva.2024.105359","DOIUrl":"10.1016/j.jmva.2024.105359","url":null,"abstract":"<div><p>A Bayesian covariance structure model (BCSM) is proposed for interval-censored multi-way nested survival data. This flexible modeling framework generalizes mixed effects survival models by allowing positive and negative associations among clustered observations. Conjugate shifted-inverse gamma priors are proposed for the covariance parameters, implying inverse gamma priors for the eigenvalues of the covariance matrix, which ensures a positive definite covariance matrix under posterior analysis. A numerically efficient Gibbs sampling procedure is defined for balanced nested designs. This requires sampling latent variables from their marginal full conditional distributions, which are derived through a recursive formula. This makes the estimation procedure suitable for interval-censored data with large cluster sizes. For unbalanced nested designs, a novel (balancing) data augmentation procedure is introduced to improve the efficiency of the Gibbs sampler. The Gibbs sampling procedure is validated in two simulation studies. The linear transformation BCSM (LT-BCSM) was applied to two-way nested interval-censored event times to analyze differences in adverse events between three groups of patients, who were randomly allocated to treatment with different stents (BIO-RESORT). The parameters of the structured covariance matrix represented unobserved heterogeneity in treatment effects and were examined to detect differential treatment effects. A comparison was made with inference results under a random effects linear transformation model. It was concluded that the LT-BCSM led to inferences with higher posterior credibility, a more profound way of quantifying evidence for risk equivalence of the three treatments, and it was more robust to prior specifications.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000666/pdfft?md5=ba8eccdffa71a651c495cfe20091f2f0&pid=1-s2.0-S0047259X24000666-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141993461","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

Conjugacy properties of multivariate unified skew-elliptical distributions 多元统一斜椭圆分布的共轭特性

IF 1.4 3区数学

Journal of Multivariate Analysis Pub Date : 2024-08-06 DOI: 10.1016/j.jmva.2024.105357

{"title":"Conjugacy properties of multivariate unified skew-elliptical distributions","authors":"","doi":"10.1016/j.jmva.2024.105357","DOIUrl":"10.1016/j.jmva.2024.105357","url":null,"abstract":"<div><p>The family of multivariate unified skew-normal (SUN) distributions has been recently shown to possess fundamental conjugacy properties. When used as priors for the vector of coefficients in probit, tobit, and multinomial probit models, these distributions yield posteriors that still belong to the SUN family. Although this result has led to important advancements in Bayesian inference and computation, its applicability beyond likelihoods associated with fully-observed, discretized, or censored realizations from multivariate Gaussian models remains yet unexplored. This article covers such a gap by proving that the wider family of multivariate unified skew-elliptical (SUE) distributions, which extends SUNs to more general perturbations of elliptical densities, guarantees conjugacy for broader classes of models, beyond those relying on fully-observed, discretized or censored Gaussians. Such a result leverages the closure under linear combinations, conditioning and marginalization of SUE to prove that this family is conjugate to the likelihood induced by regression models for fully-observed, censored or dichotomized realizations from skew-elliptical distributions. This key advancement enlarges the set of models that enable conjugate Bayesian inference to general formulations arising from elliptical and skew-elliptical families, including the multivariate Student’s <span><math><mi>t</mi></math></span> and skew-<span><math><mi>t</mi></math></span>, among others.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142148580","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