[SOLVED] ECON772 Homework 1 -Asymptotics

• 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 di⁄erentiable 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.