Question

- Find the estimator of
*σ^2*,*σ^**2**=ρ**S^2*(where*ρ*is a constant multiplier) that minimizes the MSE. Useful facts:*E(**S^**2)**=**σ^**2**,**E(**ρ**S^**2)**= ρ**σ^**2**, Var(**ρ**S^**2)**=**ρ^**2**Var(**S^**2)*and*Var(**S^**2)**=(**2**σ^4)/**n-1*. Express MSE as a function of*ρ*and and find the value of*ρ*that minimizes this expression. (Hint: Take the derivative with respect to , set equal to zero, solve for*ρ*, etc.)

Answer #1

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