Question

Question 6 Let X1, . . . , Xn denote a sequence of independent and identically distributed i.id. N(14x, σ2) random variables, and let Yı, . . . , Yrn denote an independent sequence of iid. Nụy, σ2) ran- dom variables. il Λί and Y is an unbiased estimator of μ for any value of λ in the unit interval, i.e. 0 < λ < 1. 2. Verify that the variance of this estimator is minimised when and determine the sampling distribution of the resulting estimator 3. If Ax-α + β and μΥ-α-β, determine a method of moments estimator for a. In what way(or ways) and under what circumstances will this estimator be equivalent to the previous estimator?

Answer 1

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