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Shrinkage estimation for mean and co...

Kubokawa, Tatsuya.

Shrinkage estimation for mean and covariance matrices

Record Type:	Electronic resources : Monograph/item
Title/Author:	Shrinkage estimation for mean and covariance matricesby Hisayuki Tsukuma, Tatsuya Kubokawa.
Author:	Tsukuma, Hisayuki.
other author:	Kubokawa, Tatsuya.
Published:	Singapore :Springer Singapore :2020.
Description:	ix, 112 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Statistical decision.
Online resource:	https://doi.org/10.1007/978-981-15-1596-5
ISBN:	9789811515965$q(electronic bk.)

Shrinkage estimation for mean and covariance matrices
Tsukuma, Hisayuki.

Shrinkage estimation for mean and covariance matrices[electronic resource] /by Hisayuki Tsukuma, Tatsuya Kubokawa. - Singapore :Springer Singapore :2020. - ix, 112 p. :ill., digital ;24 cm. - SpringerBriefs in statistics, JSS research series in statistics. - SpringerBriefs in statistics.JSS research series in statistics..

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.

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.

ISBN: 9789811515965$q(electronic bk.)

Standard No.: 10.1007/978-981-15-1596-5doiSubjects--Topical Terms:

181911
Statistical decision.

LC Class. No.: QA279.4 / .T785 2020

Dewey Class. No.: 519.542

Shrinkage estimation for mean and covariance matrices
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505 0 $a 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.
520 $a 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.
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