Question: 7. Let X be a random variable with mean and variance 2. You want to estimate under SEL, and propose an estimate of

7. Let X be a random variable with mean μ and variance σ2. You want to estimate μ under SEL, and propose an estimate of the form (1 − b)X.

(a) Find b∗, the b that minimizes the MSE.

(Hint: Use the “variance + (bias)2” representation of MSE.)

(b) Discuss the dependence of b∗ on μ and σ2 and its implications on the role of shrinkage in estimation.

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