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

Rivas-Martínez, GI; Jiménez Gamero, María Dolores

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 L-2 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.

Year:

2018

Type of Publication:

Article

Keywords:

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

Journal:

Revstat-Statistical Journal

Volume:

16

Number:

1

Pages:

137-166

Month:

January

Note:

Q4 115/123 h-index 0.436 (JCR2017)

Comments:

MTM2014-55966-P and MTM2017-89422-P