Statistics Graduate Level Quiz
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STATISTICAL INFERENCE
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Two estimators of θ\theta satisfy E(T1)−θ=1E(T_1)-\theta=1, E(T2)−θ=−1E(T_2)-\theta=-1, Var⁡(T1)=4\operatorname{Var}(T_1)=4, Var⁡(T2)=1\operatorname{Var}(T_2)=1, and Cov⁡(T1,T2)=1\operatorname{Cov}(T_1,T_2)=1. For Ta=aT1+(1−a)T2T_a=aT_1+(1-a)T_2, where aa may be any real number, which value of aa minimizes the mean squared error of TaT_a?
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