<電子ブック>
Shrinkage Estimation for Mean and Covariance Matrices / by Hisayuki Tsukuma, Tatsuya Kubokawa
(JSS Research Series in Statistics. ISSN:23640065)
版 | 1st ed. 2020. |
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出版者 | Singapore : Springer Nature Singapore : Imprint: Springer |
出版年 | 2020 |
本文言語 | 英語 |
大きさ | IX, 112 p. 1 illus : online resource |
著者標目 | *Tsukuma, Hisayuki author Kubokawa, Tatsuya author SpringerLink (Online service) |
件 名 | LCSH:Biometry LCSH:Statistics FREE:Biostatistics FREE:Statistical Theory and Methods |
一般注記 | 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 HTTP:URL=https://doi.org/10.1007/978-981-15-1596-5 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9789811515965 |
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EB00238543 |
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