[4:08 p. m., 10/7/2021] Ejh: 4. Let be i.i.d. normal variable following the distribution , where is the mean and is the variance.

Question

Denote by and the maximum likelihood estimators of and respectively based on the i.i.d. observations .
(In our usual notation, . We use in this problem to make clear that the parameter being estimated is not .)
(a)
1 punto posible (calificable, resultado oculto)
Is the estimator of asymptotically normal?
yes
no
[4:27 p. m., 10/7/2021] Ejh: Let
g(u,t)=2u^2+t
and let be the Fisher information matrix of X1~N(u,t)
The asymptotic variance of is...
• Nabla g(u,t)^T I(u,t) nabla(u,t)
•Nabla g(u,t)^T (I(u,t)^-1 Nabla g(u,t)
•Nabla g(u,t)^T I(u,t)
•Nabla g(u,t)^T(I(u,t))



c. Using the results from above and referring back to homework solutions if necessary, compute the asymptotic variance of the estimator .
Hint: The inverse of a diagonal matrix where is the diagonal matrix .

V(2u^2+t) or the estimator 2u^2+t

Usar la inversa de (a 0, 0 a) es (1/a 0, 0 1/a)

Answer 1

yes

second

16*mu^2*tau+2*tau^2