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.
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Akritas et al. (2001) studied this question.