Overview
- Integrates modern and classical shrinkage estimation and contributes to further developments in the field
- Provides a unified approach to low- and high-dimensional models with respect to the size of the mean matrix
- Presents recent results of high-dimensional generalization of decision-theoretic estimation of the covariance matrix
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book provides a self-contained introduction to shrinkage estimation for matrix-variate normal distribution models. More specifically, it presents recent techniques and results in estimation of mean and covariance matrices with a high-dimensional setting that implies singularity of the sample covariance matrix. Such high-dimensional models can be analyzed by using the same arguments as for low-dimensional models, thus yielding a unified approach to both high- and low-dimensional shrinkage estimations. The unified shrinkage approach not only integrates modern and classical shrinkage estimation, but is also required for further development of the field. Beginning with the notion of decision-theoretic estimation, this book explains matrix theory, group invariance, and other mathematical tools for finding better estimators. It also includes examples of shrinkage estimators for improving standard estimators, such as least squares, maximum likelihood, and minimum risk invariantestimators, and discusses the historical background and related topics in decision-theoretic estimation of parameter matrices. This book is useful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics.
Authors and Affiliations
About the authors
Tatsuya Kubokawa, Faculty of Economics, University of Tokyo
Bibliographic Information
Book Title: Shrinkage Estimation for Mean and Covariance Matrices
Authors: Hisayuki Tsukuma, Tatsuya Kubokawa
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-15-1596-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
Softcover ISBN: 978-981-15-1595-8Published: 17 April 2020
eBook ISBN: 978-981-15-1596-5Published: 16 April 2020
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: IX, 112
Number of Illustrations: 1 b/w illustrations
Topics: Statistics for Life Sciences, Medicine, Health Sciences, Statistical Theory and Methods, Biostatistics