st: Challenging Econometrics Questions

["Dave Jackson" <quinner8004@hotmail.com>]

The salary of Canadian persons has mean � and variance σ^2.
Two independent samples are drawn, one is of size m and the other of size n.
Let the sample means be �Xn and �Xm. Now consider the two estimators of �

�1 = 2/3X(bar)m + 1/3X(bar)n

�2 = m/m+n X(bar)m + n/m+n X(bar)n


(a) Show that both estimators are unbiased.
(b) Derive the variance of each of the estimator
(c) Derive the mean squared error of these estimator
(d) Suppose that m = n which estimator is more efficient

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