Estimation of the error distribution in a varying coefficient regression model

Abstract

This paper deals with the estimation of the error distribution function in a varying coefficient regression model. We propose two estimators and study their asymptotic properties by obtaining uniform stochastic expansions. The first estimator is a residual-based empirical distribution function. We study this estimator when the varying coefficients are estimated by under-smoothed local quadratic smoothers. Our second estimator which exploits the fact that the error distribution has mean zero is a weighted residual-based empirical distribution whose weights are chosen to achieve the mean zero property using empirical likelihood methods. The second estimator improves on the first estimator. Bootstrap confidence bands based on the two estimators are also discussed.

Keywords:

• Uniform stochastic expansions
• nonparametric residuals
• local quadratic smoothers
• B-splines
• confidence band

Acknowledgments

We thank the referees for helpful comments that improved the paper and for insisting to generalise the results of the paper from the model with p=1 to the present one with general dimension p.

Disclosure statement

No potential conflict of interest was reported by the authors.