]RI. 18) for proper p and X. Under various but very general conditions on X, F and 'fjJ, the estimator Mn is asymptotically normal, as n -> 00 and for fixed p. 14), Q~,f2(Mn - (3) where 2 0- E. 22) The conditions that we need to impose on F to obtain the asymptotic normality of Mn are remarkably weak under some functions 'fjJ; for instance, if'fjJ is a nondecreasing step-function, then the derivative of F should exist only in a neighborhood of jump points of 'fjJ.

56) as n ---. 00. 56)), the event sn = could happen for a small n; then sn should be replaced by an arbitrary small fixed constant. l) k : JR1 f-> JR1 has a compact support, is continuous on its support and 1/ f(O). Choose a kernel function k : JR1 J J k(x)dx = 0, xk(x)dx = -l. 57) where the sequence lin -> {lIn}~=l 0, nll; satisfies and nll~ -> 00 -> ° as n -> 00. 59) ) , 1~ k(y)dy. 62) The detailed proof of these properties can be found in Chapter 10. Quite analogously, we could estimate 1/ f(F- 1 (a)) for any a E [0,1].