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There are a lot of symbols so I am sorry if this is hard to read.

Q=theta hat, q=theta

Suppose E(Q1)=E(Q2)=q. V(Q1)=(sigma1)^2, V(Q2)=(sigma2)^2. Consider the estimator Q3=aQ1+(1-a)Q2.

a)Show that Q3 is an unbiased estimator for q.

b) If Q1 and Q2 are independent, how should the constant a be chosen in order to minimize the variance of Q3?

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Statistics and Probability, Statistics

Category:- Statistics and Probability
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