Shrinkage Estimation for Mean and Covariance Matrices by Hisayuki Tsukuma & Tatsuya Kubokawa

Author:Hisayuki Tsukuma & Tatsuya Kubokawa
Language: eng
Format: epub
ISBN: 9789811515965
Publisher: Springer Singapore

Next, we treat the case of . Assume that the prior distribution of is , where is unknown. Then the posterior distribution of and the marginal distribution of are, respectively,

where . The resulting posterior mean of becomes . Since we need to estimate , it will be estimated from the marginal distributions of and . Then from Corollary 3.​1, , and we think of as an estimator of , where c is a positive constant. Thus the resulting Efron-Morris (1972) type empirical Bayes estimator of for can be expressed as

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