Take the Bernoulli model.

(a) Find the asymptotic variance of theMLE. (Hint: see Exercise 10.8.)

(b) Propose an estimator of the asymptotic variance V .

(c) Show that this estimator is consistent for V as n!1.

(d) Propose a standard error s( b p) for the MLE b p. (Recall that the standard error is supposed to approximate the variance of b p, not that of the variance of p n( b p ¡ p). What would be a reasonable approximation of the variance of b p once you have a reasonable approximation of the variance of p n( b p ¡p) from part (b)? )