34. The mean squared error of an estimator is MSE() E( )2....

34. The mean squared error of an estimator ˆ

 is MSE(ˆ)

E(

ˆ  )2. If ˆ is unbiased, then MSE(ˆ)
V(ˆ), but in general MSE(

ˆ)
V(ˆ) (bias)2. Consider the estimator

ˆ 2
KS2, where S2
sample variance. What value of K minimizes the mean squared error of this estimator when the population distribution is normal? [Hint: It can be shown that E[(S2

)2

]
(n 1)4

/(n  1)

In general, it is difficult to find ˆ

 to minimize MSE(ˆ

), which is why we look only at unbiased estimators and minimize V(ˆ

).]