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Keywords:

  • asymptotic representation;
  • goodness-of-fit;
  • non-parametric regression residuals;
  • prediction intervals;
  • residual distribution;
  • weak convergence

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.