A Misspecified Model

where 0 is the beginning value for the iteration, 6 is the updated parameter vector, H is an estimate of H, and X is a scalar step size that determines the length of the step taken in the directions of search d = —(H)~dQn(S)/d6. Consider the asymptotic properties of 0 obtained from (2) without further iteration, assuming that 0 is consistent for 0O, V«(0 0O) is bounded in probability, and plim(AT) = H. 1. Show that if plim(X) = 1, then 0 and 0 are asymptotically equivalent (i.e., -Jn(9 — 9) converges in probability to zero). 2. Consider a choice of step size X as the solution to