查看更多>>摘要：We consider the quadratic classification for high-dimensional data under the strongly spiked eigenvalue (SSE) model. High-dimensional data contain much information, however, it also contains huge amount of noise. We detect the high-dimensional noise as a spiked eigenstructure of high-dimensional covariance matrices. In order to find the difference between two populations, we utilize a geometric feature of high-dimensional data. The classification analysis based on the geometric feature of high-dimensional data is called geometrical quadratic discriminant analysis (GQDA). We create new GQDA on the basis of the high-dimensional spiked eigenstructures. We precisely study the influence of the spiked eigenstructure on GQDA using several examples. In order to remove the spiked noise, we use a data transformation technique. We show that our proposed classifier has a consistency property with respect to the error rate of misclassifying an individual. By using computer simulation, we discuss the performance of the proposed classifier. Finally, we give several demonstrations of data analysis using a microarray data set. (C) 2021 The Author(s). Published by Elsevier Inc.
查看更多>>摘要：Functional data analysis (FDA), which is a branch of statistics on modeling infinite dimensional random vectors resided in functional spaces, has become a major research area for Journal of Multivariate Analysis. We review some fundamental concepts of FDA, their origins and connections from multivariate analysis, and some of its recent developments, including multi-level functional data analysis, high-dimensional functional regression, and dependent functional data analysis. We also discuss the impact of these new methodology developments on genetics, plant science, wearable device data analysis, image data analysis, and business analytics. Two real data examples are provided to motivate our discussions. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Multivariate linear regression analysis is an important technique for modeling the predictive relationships of multiple related response variables on a set of common predictor variables. Numerous studies have been conducted on situations where response variables are given and only predictor variables are subject to variable selection. In practice, however, some response variables do not depend on any of the predictor variables and have very small regression coefficients, implying that response variables need to be selected. Several methods have been proposed for response variable selection in multivariate linear regression. Examples include Bonferroni selection, linear step-up selection, adaptive linear step-up selection, multiple-stage linear step-up selection, response best subset selection and sparse envelope selection. In this article, we address some aspects of response variable selection focusing on the above-mentioned examples concerning methodological developments, theoretical properties and computational algorithms. We address their performances under the recall rate or true positive rate, true negative rate, precision rate, F-measure, model size and their standard deviations via simulation studies. We also highlight two issues that require further study. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Change point analysis aims to detect structural changes in a data sequence. It has always been an active research area since it was introduced in the 1950s. In modern statistical applications, however, high-throughput data with increasing dimensions are ubiquitous in fields ranging from economics, finance to genetics and engineering. For those problems, the earlier works are typically no longer applicable. As a result, the problem of testing a change point for high dimensional data sequences has been an important yet challenging task. In this paper, we first focus on models for at most one change point, and review recent state-of-art techniques for change point testing of high dimensional mean vectors and compare their theoretical properties. Based on that, we provide a survey of some extensions to general high dimensional parameters beyond mean vectors as well as strategies for testing multiple change points in high dimensions. Finally, we discuss some open problems for possible future research directions. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we review recent developments in high-dimensional consistencies of KOO methods for selection of variables in multivariate regression models and discriminant analysis models. The KOO methods considered are mainly based on general information criteria, but we take up also KOO methods based on some other selection methods. Some references are given for high-dimensional consistencies in some other multivariate models. (C) 2021 Published by Elsevier Inc.
查看更多>>摘要：Hypothesis testing is one of the fundamental paradigms of statistical inference. The three canonical hypothesis testing procedures available in the statistical literature are the likelihood ratio (LR) test, the Wald test and the Rao (score) test. All of them have good optimality properties and past research has not identified any of these three procedures to be a clear winner over the other two. However, the classical versions of these tests are based on the maximum likelihood estimator (MLE), which, although the most optimal estimator asymptotically, is known for its lack of robustness under outliers and model misspecification. In the present paper we provide an overview of the analogues of these tests based on the minimum density power divergence estimator (MDPDE), which presents us with an alternative option that is strongly robust and highly efficient. Since these tests have, so far, been mostly studied for univariate responses, here we primarily focus on their performances for several important hypothesis testing problems in the multivariate context under the multivariate normal model family. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The literature on non-normal model-based clustering has continued to grow in recent years. The non-normal models often take the form of a mixture of component densities that offer a high degree of flexibility in distributional shapes. They handle skewness in different ways, most typically by introducing latent 'skewing' variable(s), while some other consider marginal transformations of the original variable(s). We provide a selective overview of the main types of skew distributions used in the area, based on their characterization of skewness, and discuss different skew shapes they can produce. For brevity, we focus on the more commonly-used families of distributions. Crown Copyright (C) 2021 Published by Elsevier Inc. All rights reserved.
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