Journal of Multivariate Analysis最新文献

{"title":"The inner partial least square: An exploration of the “necessary” dimension reduction","authors":"Yunjian Yin,&nbsp;Lan Liu","doi":"10.1016/j.jmva.2024.105356","DOIUrl":"10.1016/j.jmva.2024.105356","url":null,"abstract":"<div><p>The partial least square (PLS) algorithm retains the combinations of predictors that maximize the covariance with the outcome. Cook et al. (2013) showed that PLS results in a predictor envelope, which is the smallest reducing subspace of predictors’ covariance that contains the coefficient. However, PLS and predictor envelope both target at a space that contains the regression coefficients and therefore they may sometimes be too conservative to reduce the dimension of the predictors. In this paper, we propose a new method that may improve the estimation efficiency of regression coefficients when both PLS and predictor envelope fail to do so. Specifically, our method results in the largest reducing subspace of predictors’ covariance that is contained in the coefficient matrix space. Interestingly, the moment based algorithm of our proposed method can be achieved by changing the max in PLS to min. We define the modified PLS as the inner PLS and the resulting space as the inner predictor envelope space. We provide the theoretical properties of our proposed methods as well as demonstrate their use in China Health and Nutrition Survey.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105356"},"PeriodicalIF":1.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083637","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":"Cross projection test for mean vectors via multiple random splits in high dimensions","authors":"Guanpeng Wang ,&nbsp;Jiujing Wu ,&nbsp;Hengjian Cui","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":"204 ","pages":"Article 105358"},"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}

{"title":"Bayesian covariance structure modeling of interval-censored multi-way nested survival data","authors":"Stef Baas ,&nbsp;Jean-Paul Fox ,&nbsp;Richard J. Boucherie","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":"204 ","pages":"Article 105359"},"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}

{"title":"Conjugacy properties of multivariate unified skew-elliptical distributions","authors":"Maicon J. Karling ,&nbsp;Daniele Durante ,&nbsp;Marc G. Genton","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":"204 ","pages":"Article 105357"},"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}

{"title":"Mean and covariance estimation for discretely observed high-dimensional functional data: Rates of convergence and division of observational regimes","authors":"Alexander Petersen","doi":"10.1016/j.jmva.2024.105355","DOIUrl":"10.1016/j.jmva.2024.105355","url":null,"abstract":"<div><p>Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which <span><math><mi>p</mi></math></span>, the number of curves per subject, is often much larger than the sample size <span><math><mi>n</mi></math></span>. In this setting of high-dimensional functional data, much of developed methodology relies on preliminary estimates of the unknown mean functions and the auto- and cross-covariance functions. This paper investigates the convergence rates of local linear estimators in terms of the maximal error across components and pairs of components for mean and covariance functions, respectively, in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and uniform metrics. The local linear estimators utilize a generic weighting scheme that can adjust for differing numbers of discrete observations <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span> across curves <span><math><mi>j</mi></math></span> and subjects <span><math><mi>i</mi></math></span>, where the <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span> vary with <span><math><mi>n</mi></math></span>. Particular attention is given to the equal weight per observation (OBS) and equal weight per subject (SUBJ) weighting schemes. The theoretical results utilize novel applications of concentration inequalities for functional data and demonstrate that, similar to univariate functional data, the order of the <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span> relative to <span><math><mi>p</mi></math></span> and <span><math><mi>n</mi></math></span> divides high-dimensional functional data into three regimes (sparse, dense, and ultra-dense), with the high-dimensional parametric convergence rate of <span><math><msup><mrow><mfenced><mrow><mo>log</mo><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow><mo>/</mo><mi>n</mi></mrow></mfenced></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> being attainable in the latter two.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105355"},"PeriodicalIF":1.4,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141953976","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":"Dependent censoring with simultaneous death times based on the Generalized Marshall–Olkin model","authors":"Mikael Escobar-Bach,&nbsp;Salima Helali","doi":"10.1016/j.jmva.2024.105347","DOIUrl":"10.1016/j.jmva.2024.105347","url":null,"abstract":"<div><p>In this paper, we consider the problem of dependent censoring models with a positive probability that the times of failure are equal. In this context, we propose to consider the Marshall–Olkin type model and studied some properties of the associated survival copula in its application to censored data. We also introduce estimators for the marginal distributions and the joint survival probabilities under different schemes and show their asymptotic normality under appropriate conditions. Finally, we evaluate the finite-sample performance of our approach relying on a small simulation study with synthetic data real data applications.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105347"},"PeriodicalIF":1.4,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X2400054X/pdfft?md5=b9e7bd9d7773367d73bd57f13743392a&pid=1-s2.0-S0047259X2400054X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947950","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":"Two-sample test for high-dimensional covariance matrices: A normal-reference approach","authors":"Jingyi Wang ,&nbsp;Tianming Zhu ,&nbsp;Jin-Ting Zhang","doi":"10.1016/j.jmva.2024.105354","DOIUrl":"10.1016/j.jmva.2024.105354","url":null,"abstract":"<div><p>Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required assumptions are not satisfied which attests that they are not always applicable in real data analysis. To overcome this difficulty, a normal-reference test is proposed and studied in this paper. It is shown that under some regularity conditions and the null hypothesis, the proposed test statistic and a chi-squared-type mixture have the same limiting distribution. It is then justified to approximate the null distribution of the proposed test statistic using that of the chi-squared-type mixture. The distribution of the chi-squared-type mixture can be well approximated using a three-cumulant matched chi-squared-approximation with its approximation parameters consistently estimated from the data. The asymptotic power of the proposed test under a local alternative is also established. Simulation studies and a real data example demonstrate that the proposed test works well in general scenarios and outperforms the existing competitors substantially in terms of size control.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105354"},"PeriodicalIF":1.4,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871513","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":"An approximation to peak detection power using Gaussian random field theory","authors":"Yu Zhao ,&nbsp;Dan Cheng ,&nbsp;Armin Schwartzman","doi":"10.1016/j.jmva.2024.105346","DOIUrl":"10.1016/j.jmva.2024.105346","url":null,"abstract":"<div><p>We study power approximation formulas for peak detection using Gaussian random field theory. The approximation, based on the expected number of local maxima above the threshold <span><math><mi>u</mi></math></span>, <span><math><mrow><mi>E</mi><mrow><mo>[</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span>, is proved to work well under three asymptotic scenarios: small domain, large threshold, and sharp signal. An adjusted version of <span><math><mrow><mi>E</mi><mrow><mo>[</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span> is also proposed to improve accuracy when the expected number of local maxima <span><math><mrow><mi>E</mi><mrow><mo>[</mo><msub><mrow><mi>M</mi></mrow><mrow><mo>−</mo><mi>∞</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span> exceeds 1. Cheng and Schwartzman (2018) developed explicit formulas for <span><math><mrow><mi>E</mi><mrow><mo>[</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span> of smooth isotropic Gaussian random fields with zero mean. In this paper, these formulas are extended to allow for rotational symmetric mean functions, making them applicable not only for power calculations but also for other areas of application that involve non-centered Gaussian random fields. We also apply our formulas to 2D and 3D simulated datasets, and the 3D data is induced by a group analysis of fMRI data from the Human Connectome Project to measure performance in a realistic setting.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105346"},"PeriodicalIF":1.4,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871667","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":"Double penalized variable selection for high-dimensional partial linear mixed effects models","authors":"Yiping Yang,&nbsp;Chuanqin Luo,&nbsp;Weiming Yang","doi":"10.1016/j.jmva.2024.105345","DOIUrl":"10.1016/j.jmva.2024.105345","url":null,"abstract":"<div><p>In this study, we address the selection of both fixed and random effects in partial linear mixed effects models. By combining B-spline and QR decomposition techniques, we propose a double-penalized likelihood procedure for both estimating and selecting these effects. Furthermore, we introduce an orthogonality-based method to estimate the non-parametric component, ensuring that the fixed and random effects are separated without any mutual interference. The asymptotic properties of the resulting estimators are investigated under mild conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. Finally, we demonstrate the practical applicability of our methodology by analyzing a real data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105345"},"PeriodicalIF":1.4,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141630322","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":"Stochastic hyperplane-based ranks and their use in multivariate portmanteau tests","authors":"Šárka Hudecová ,&nbsp;Miroslav Šiman","doi":"10.1016/j.jmva.2024.105344","DOIUrl":"10.1016/j.jmva.2024.105344","url":null,"abstract":"<div><p>The article proposes and justifies an optimal rank-based portmanteau test of multivariate elliptical strict white noise against multivariate serial dependence. It is based on new stochastic hyperplane-based ranks that are simpler and easier to compute than other usable hyperplane-based competitors and still share with them many good properties such as their distribution-free nature, affine invariance, efficiency, robustness and weak moment assumptions. The finite-sample performance of the portmanteau test is illustrated empirically in a small Monte Carlo simulation study.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"204 ","pages":"Article 105344"},"PeriodicalIF":1.4,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785479","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}