Computationally Efficient Goodness-of-Fit Tests for the Error Distribution in Nonparametric Regression

Authors

  • G.I. Rivas-Martínez Universidad Nacional de Asunción
  • Maria Dolores Jiménez-Gamero Universidad de Sevilla

DOI:

https://doi.org/10.57805/revstat.v16i1.236

Keywords:

goodness-of-fit, empirical characteristic function, regression residuals, weighted bootstrap, consistency

Abstract

Several procedures have been proposed for testing goodness-of-fit to the error distribution in nonparametric regression models. The null distribution of the associated test statistics is usually approximated by means of a parametric bootstrap which, under certain conditions, provides a consistent estimator. This paper considers a goodness-of-fit test whose test statistic is an L2 norm of the difference between the empirical characteristic function of the residuals and a parametric estimate of the characteristic function in the null hypothesis. It is proposed to approximate the null distribution through a weighted bootstrap which also produces a consistent estimator of the null distribution but, from a computational point of view, is more efficient than the parametric bootstrap.

Published

2018-02-07

How to Cite

Rivas-Martínez , G., & Jiménez-Gamero , M. D. (2018). Computationally Efficient Goodness-of-Fit Tests for the Error Distribution in Nonparametric Regression. REVSTAT-Statistical Journal, 16(1), 137–166. https://doi.org/10.57805/revstat.v16i1.236