Question: Let Y denote the sample average from a random sample with mean m and variance s2. Consider two alternative estimators of m: (i) Show that

Let Y̅ denote the sample average from a random sample with mean m and variance s2. Consider two alternative estimators of m:

(i) Show that W₁ and W₂ are both biased estimators of m and find the biases. What happens to the biases as n ® ∝? Comment on any important differences in bias for the two estimators as the sample size gets large.

(ii) Find the probability limits of W₁ and W₂. Which estimator is consistent?

(iii) Find Var (W₁) and Var (W₂).

(iv) Argue that W₁ is a better estimator than Y if m is “close” to zero. (Consider both bias and variance.)

u: W, = [(n 1)/n]Y and W, = Y/2. %3D %3D

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i W1 and W2 are both biased estimators of m The bias of W1 is given by BiasW1 EW1 m En 1 nY m n 1 nE... View full answer

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