7 1 For the situation of Example 7 1 (a) The empirical Bayes estimator of , using an unbiased estimate of 2 (2 2), is EB 1 (p 2)2 x 2 x, the James Stein estimator (b) The empirical Bayes estimator of , using the marginal MLE of 2 (2 2), is EB 1 p2 x 2 x, which resembles the positive part Stein esti...

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7.1 For the situation of Example 7.1: (a) The empirical Bayes estimator of , using an...

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7.1 For the situation of Example 7.1:

(a) The empirical Bayes estimator of θ , using an unbiased estimate of τ 2/(σ2 + τ 2), is

δEB =

1 − (p − 2)σ2

|x|

x, the James-Stein estimator.

(b) The empirical Bayes estimator of θ , using the marginal MLE of τ 2/(σ2 + τ 2), is

δEB =

1 − pσ2

|x|

x, which resembles the positive-part Stein estimator.

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Theory Of Point Estimation

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Authors: Erich L. Lehmann, George Casella

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7.1 For the situation of Example 7.1: (a) The empirical Bayes estimator of , using an...

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