On hadamard differentiability of extended statistical functional

Abstract

It has been shown ([6], Ph.D. dissertation, Harvard University) that the remainder term of a form of the Taylor expansion, involving Hadamard derivative, of the statistical functional is asymptotically negligible. This result is extended to a more general form with respect to weighted empirical processes in order to establish some (uniform) linear functional approximations, which is usually needed for drawing statistical conclusions (in a large sample).extended statistical functional Hadamard differentiability robust (M-)estimation statistical functional uniform asymptotic linearity weighted empirical processes