• Let

H0 : X 2n vs. HA : X 2n

with n large. Construct a test statistic using an asymptotic approximation for the distribution of X.

• Let S_n be a statistic with plim S_n = . Let g ( ) be a dierentiable function. Prove from rst principals that

plim g (S_n) = g ( ):

• Let

:

Show that

does not converge to a nite matrix as T !1. Find a matrix D_T such that

converges to a nite full-rank matrix as T !1.