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Shrinkage estimation for mean and co...

Tsukuma, Hisayuki.

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Shrinkage estimation for mean and covariance matrices

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Shrinkage estimation for mean and covariance matrices/ by Hisayuki Tsukuma, Tatsuya Kubokawa.
作者:	Tsukuma, Hisayuki.
其他作者:	Kubokawa, Tatsuya.
出版者:	Singapore :Springer Singapore : : 2020.,
面頁冊數:	ix, 112 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Statistical decision. -
電子資源:	https://doi.org/10.1007/978-981-15-1596-5
ISBN:	9789811515965

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

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

533208
Statistical decision.

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

Dewey Class. No.: 519.542

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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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