Consistency for the least squares estimator in nonparametric regression

Abstract

We shall study the general regression model Y = g0(X) + ε, where X and ε are independent. The available information about g0 can be expressed by g0 ∈ script G sign for some class script G sign. As an estimator of g0 we choose the least squares estimator. We shall give necessary and sufficient conditions for consistency of this estimator in terms of (basically) geometric properties of script G sign. Our main tool will be the theory of empirical processes.