JSS Research Series in Statistics

Shrinkage Estimation for Mean and Covariance Matrices

Authors: Tsukuma, Hisayuki, Kubokawa, Tatsuya

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  • 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
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  • ISBN 978-981-15-1596-5
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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 invariant estimators, 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.

About the authors

Hisayuki Tsukuma, Faculty of Medicine, Toho University
Tatsuya Kubokawa, Faculty of Economics, University of Tokyo

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-981-15-1596-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Shrinkage Estimation for Mean and Covariance Matrices
Authors
Series Title
JSS Research Series in Statistics
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-1596-5
DOI
10.1007/978-981-15-1596-5
Softcover ISBN
978-981-15-1595-8
Series ISSN
2364-0057
Edition Number
1
Number of Pages
IX, 112
Number of Illustrations
1 b/w illustrations
Topics