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Shrinkage Estimation for Mean and Covariance Matrices: SpringerBriefs in Statistics

Autor Hisayuki Tsukuma, Tatsuya Kubokawa
en Limba Engleză Paperback – 17 apr 2020
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.
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Specificații

ISBN-13: 9789811515958
ISBN-10: 9811515956
Pagini: 112
Ilustrații: IX, 112 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.2 kg
Ediția:1st ed. 2020
Editura: Springer Nature Singapore
Colecția Springer
Seriile SpringerBriefs in Statistics, JSS Research Series in Statistics

Locul publicării:Singapore, Singapore

Cuprins

Preface.- Decision-theoretic approach to estimation.- Matrix theory.- Matrix-variate distributions.- Multivariate linear model and invariance.- Identities for evaluating risk.- Estimation of mean matrix.- Estimation of covariance matrix.- Index.


Notă biografică

Hisayuki Tsukuma, Faculty of Medicine, Toho University

Tatsuya Kubokawa, Faculty of Economics, University of Tokyo

Textul de pe ultima copertă

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.

Caracteristici

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