Non‐parametric Estimation of the Residual Distribution

Abstract

Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are “smooth”, and ε is independent of X . An estimator of the distribution of ε based on non‐parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness‐of‐fit tests are discussed.