Let S 2 be the sample variance of a random sample of size n 1 from N(, ), 0 , where is known We know E(S 2 ) (a) What is the efficiency of S 2 (b) Under these conditions, what is the mle of (c) What is the asymptotic distribution of n( ) ...

a ES2 Therefore En S2 n CovS2 S2 En S2 n S2 0 Therefore VarS2 n12 So VarS2ES2 23 which ...

Let S 2 be the sample variance of a random sample of size n > 1 from

Question:

Let S² be the sample variance of a random sample of size n > 1 from N(μ, θ), 0 < θ < ∞, where μ is known. We know E(S²) = θ.
(a) What is the efficiency of S²?
(b) Under these conditions, what is the mle ^{^}θ of θ?
(c) What is the asymptotic distribution of √n(^{^}θ − θ)?