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Shrinkage Estimation for Mean and Covariance MatricesDecision-Theoretic Approach to Estimation

Shrinkage Estimation for Mean and Covariance Matrices: Decision-Theoretic Approach to Estimation [Statistical decision theory has been studied from around the 1940s and the researchers have already been producing many remarkable results. In the field of decision-theoretic estimation, the most surprising result is the inadmissibility of the sample mean vector in estimation of a mean vector of multivariate normal distribution. The inadmissibility result is closely relevant to the discovery of shrinkage estimator. This chapter summarizes basic terminology of decision-theoretic estimation and shrinkage estimators in the multivariate normal mean estimation. Also, Stein’s unbiased estimate of risk is briefly explained as a general method of how to find better estimators. The unbiased risk estimate method is applied to estimation of mean and covariance matrices discussed in this book.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Shrinkage Estimation for Mean and Covariance MatricesDecision-Theoretic Approach to Estimation

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Publisher
Springer Singapore
Copyright
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-15-1595-8
Pages
1 –5
DOI
10.1007/978-981-15-1596-5_1
Publisher site
See Chapter on Publisher Site

Abstract

[Statistical decision theory has been studied from around the 1940s and the researchers have already been producing many remarkable results. In the field of decision-theoretic estimation, the most surprising result is the inadmissibility of the sample mean vector in estimation of a mean vector of multivariate normal distribution. The inadmissibility result is closely relevant to the discovery of shrinkage estimator. This chapter summarizes basic terminology of decision-theoretic estimation and shrinkage estimators in the multivariate normal mean estimation. Also, Stein’s unbiased estimate of risk is briefly explained as a general method of how to find better estimators. The unbiased risk estimate method is applied to estimation of mean and covariance matrices discussed in this book.]

Published: Apr 17, 2020

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