Non-parametric applications of an infinite dimensional convolution theorem

TL;DR: In this article, a general approach to the statistical problem of efficient non-parametric estimation is given, based on an abstract (infinite dimensional) convolution theorem of the Hajek-Le Cam type.

Abstract: This paper gives a general approach to the statistical problem of efficient non-parametric estimation. The main tool is an abstract (infinite dimensional) convolution theorem of the Hajek-Le Cam type. This result is applied to the problems of efficiently estimating measures, quantile functions, spectral functions (of stationary processes), minimum distance functionals, M functional, and so forth.