The mean squared error of an estimator is MSE () E( )2 If is unbiased, then MSE( ) V( ), but in general MSE( ) V( ) (bias)2 Consider the estimator 2 K2, where 2 sample variance What value of K minimizes the mean squared error of this estimator when the population distribution is normal

Question: The mean squared error of an estimator ^ is MSE () - E(^ - ^)2. If ^ is unbiased, then MSE(^) = V(^), but in

The mean squared error of an estimator θ^ is MSE (θ) - E(θ^ - θ^)2. If θ^ is unbiased, then MSE(θ^) = V(θ^), but in general MSE(θ^) = V(θ^) + (bias)2. Consider the estimator σ2 = Kσ2, where σ2 = sample variance. What value of K minimizes the mean squared error of this estimator when the population distribution is normal?

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