Abstract

Modern statistical computing often requires dealing with huge data sets and speed of computing and available computer memory may become an issue. In this talk we shall present alternative ways to estimate various statistical functionals which are highly efficient and fast.

We consider GQL-estimators, very parsimonious weighted combinations of small number of order statistics corresponding to Gauss quadratures in numerical integration. Resulting estimators require a small number of operations and are asymptotically as efficient as classical estimators.

We shall also present a Partial Cross validation, an application of GQL-estimators in Cross Validation in nonparametric regression estimation, where the time necessary to find optimal parameters may be considerably reduced.