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.
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Tsukuma, H., Kubokawa, T. (2020). Decision-Theoretic Approach to Estimation. In: Shrinkage Estimation for Mean and Covariance Matrices. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-1596-5_1
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DOI: https://doi.org/10.1007/978-981-15-1596-5_1
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