Computationally Efficient Goodness-of-Fit Tests for the Error Distribution in Nonparametric Regression
DOI:
https://doi.org/10.57805/revstat.v16i1.236Keywords:
goodness-of-fit, empirical characteristic function, regression residuals, weighted bootstrap, consistencyAbstract
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.
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