N(θ,θ): MLE for a Normal where mean=variance is
a) (sqrt(4*bar(X_n^2)+1)-1)/2
and In this problem, we apply the Central Limit Theorem and the 1-dimensional Delta Method.
First, compute the limit and asymptotic variance of V(X_n^2)
The limit to which (X_n^2) converges in probability, also known as its P -limit , is
b)
unanswered
The asymptotic variance V(X_n^2) of (X_n^2), which is equal to Var(X_1^2), is
c)
Now, write theta^ as the function of (X_n^2) you found in part (a),
theta^=g((X_n^2))
and give its first derivative,g'(x) ,
d)
0
unanswered
What can you conclude about the asymptotic variance V(theta^) of theta^?
V(theta^)=?