Sieves for Nonparametric Estimation of Densities and Regressions.

Abstract : This report is about the use of least-squares for nonparametric regression and the use of maximum likelihood for nonparametric density estimation. Typically, these classical techniques fail when applied to infinite dimensional problems. Grenander's method of sieves is a method for modifying classical estimators to make them appropriate for nonclassical problems. Examples are given here of the application of this method to the problems of regression and density estimation. (Author)