THE NORMAL APPROXIMATION FOR SEMIPARAMETRIC AVERAGED DERIVATIVES

With the same normalization as that for standard parametric statistics , and centered at a parameter of interest, many semiparametric estimat es based on n observations have been shown to be root-n-consistent and asymptotically normal. In the context of semiparametric averaged deri vative estimates, we go further by showing that the rate of convergenc e of the finite-sample distribution to the normal limit distribution c an equal that of standard parametric statistics.