Strongly consistent density estimation of regression residual

Abstract

Consider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x) = E {Y|X} = xg, this paper investigates methods for estimating the density of the residual Y - m(X) from independent and identically distributed data. For heteroscedastic regression, we prove the strong universal (density-free) L1-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.