Question: Suppose that \({{T}_{1}},{{T}_{2}},{{T}_{3}}\) are independent estimators of an unknown parameter \(\theta \). If all of them are unbiased and \(\operatorname{var}\left( {{T}_{1}} \right)=2\operatorname{var}\left( {{T}_{2}} \right)=\frac{1}{2}\operatorname{var}\left( {{T}_{3}} \right)\), which one among \(\frac{1}{4}\left( {{T}_{1}}+2{{T}_{2}}+{{T}_{3}} \right)\), \(\frac{1}{6}\left( 2{{T}_{1}}+3{{T}_{2}}+{{T}_{3}} \right)\), \(\frac{1}{8}\left( {{T}_{1}}+3{{T}_{2}}+4{{T}_{3}} \right)\) should be preferred as an estimator of θ and why?

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