Question

1. Find the estimator of σ^2, σ^2=ρS^2 (where ρ is a constant multiplier) that minimizes the MSE. Useful facts: E(S^2)=σ^2, E(ρS^2) = ρσ^2, Var(ρS^2)=ρ^2Var(S^2) and Var(S^2)=(2σ^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