ECON 772 Homework 1- Asymptotics Solved

1)     Let

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

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

2)     Let Sn be a statistic with plim Sn = . Let g ( ) be a di⁄erentiable function. Prove from rst principals that

plim g (Sn) = g ( ):

3)     Let

 :

Show that

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

 

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