To estimate mu, we independently perform two samples, The resulting estimates are muhat1 and muhat2., for...
To estimate mu, we independently perform two samples, The resulting estimates are muhat1 and muhat2., for which the standard deviation is sigma1 and sigma2. We know combine the two estimators to an new one muhatstar
Muhatstar=alpha* muhat1 +beta*muhat2
i know that the muhatstar is unbiased if alpha*beta=1
To minimize the variance alpha= sigma2^2/(sigma1^2*sigma2^2) and beta=Sigma1^2/(sigma1^2*sigma2^2).
Question:
Is the variance of the new estimator smaller then muhat1 and/or muhat2?
Homework Answers
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