查看更多>>摘要：This paper deals with a sample measure of multivariate kurtosis, which is used as a test statistic in multivariate normality testing problems. We define a new multivariate sample kurtosis measure to provide a multivariate normality test for data with a twostep monotone missing structure. Furthermore, we derive its expectation and variance using a perturbation method. To evaluate the accuracy of a normal approximation, we conducted a Monte Carlo simulation for certain parameters. Finally, we present a numerical example to illustrate the proposed procedure. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In a bivariate distribution, it is sometimes easier to visualize conditional distributions of experimental variables rather than the joint distribution. In this sense, the subject of conditional specification of distributions has become an active field of research in recent years as part of multivariate analysis. In this article we summarize some of the main aspects of models with conditional specification. In addition, we highlight the most relevant aspects of these models and establish some challenges that we will face in the coming years. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Matrix differential calculus is a powerful mathematical tool in multivariate analysis and related areas such as econometrics, environmetrics, geostatistics, predictive modeling, psychometrics, and statistics in general. One of the key contributions to its development was the introduction of the differential approach, which has led to a significant number of applications. In this paper, we present a study of this approach to matrix differential calculus with some of its key results along with illustrative examples. We also present new applications of this approach in the multivariate linear model: namely in efficiency comparisons, sensitivity analysis, and local influence diagnostics. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey on methodological advances for variable selection in functional regression, which is typically a question for which both functional and multivariate ideas are crossing. More than a simple survey, this paper aims to promote even more new links between both areas. (C) 2021 Elsevier Inc. All rights reserved.
V. Mardia, KantiWiechers, HenrikEltzner, BenjaminHuckemann, Stephan F....
21页
查看更多>>摘要：Big data, high dimensional data, sparse data, large scale data, and imaging data are all becoming new frontiers of statistics. Changing technologies have created this flood and have led to a real hunger for new modeling strategies and data analysis by scientists. In many cases data are not Euclidean; for example, in molecular biology, the data sit on manifolds. Even in a simple non-Euclidean manifold (circle), to summarize angles by the arithmetic average cannot make sense and so more care is needed. Thus non-Euclidean settings throw up many major challenges, both mathematical and statistical. This paper will focus on the PCA and clustering methods for some manifolds. Of course, the PCA and clustering methods in multivariate analysis are one of the core topics. We basically deal with two key manifolds from a practical point of view, namely spheres and tori. It is well known that dimension reduction on non-Euclidean manifolds with PCA-like methods has been a challenging task for quite some time but recently there has been some breakthrough. One of them is the idea of nested spheres and another is transforming a torus into a sphere effectively and subsequently use the technology of nested spheres PCA. We also provide a new method of clustering for multivariate analysis which has a fundamental property required for molecular biology that penalizes wrong assignments to avoid chemically no go areas. We give various examples to illustrate these methods. One of the important examples includes dealing with COVID-19 data.
查看更多>>摘要：Principal component analysis (PCA) is one of the most widely used multivariate techniques. A little more than 50 years ago I first encountered PCA and it has played an important role in my career and beyond, for many years since. I have been persuaded that an account of my 50-year journey through time with PCA would be a suitable topic for inclusion in the Jubilee Issue of JMVA and this is the result. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We extend a concept of ANOVA broader than the traditional variance component models to MANOVA. Within this framework we can derive a spectral principal component analysis (PCA) and see how it generalises the same notion for weakly stationary vector time series. We then attempt to obtain analogous results for arrays of random variables over (i.e., indexed by the nodes of) binary trees, with only partial success. While there is an analogue of ANOVA and MANOVA for binary trees, the existence of spectral PCA there is unresolved. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The authors reminisce on their association with P.R. Krishnaiah, renowned professor of statistics at the University of Pittsburgh and founding editor of the Journal of Multivariate Analysis. They recount their individual associations with him, mainly involving the behavior of eigenvalues of random matrices, and outline two areas of applied work he performed with one of the authors. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In the last two decades or so, much work has been dedicated to the portion of distribution theory stemming from the skew-normal distribution and its ramification. This contribution presents an outline of the theme, without attempting a detailed review, which would be unfeasible, given the amount of available material. The aim is to present a panoramic view of the theme, leaving out the fine details, with rather more emphasis on the evolution of the underlying ideas and on the breath of the overall developments, as for range of specific directions considered. (C) 2021 Elsevier Inc. All rights reserved.
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