Change-point tests for the error distribution in nonparametric regression
(2006) , 30 pages
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- Abstract
- In this paper several testing procedures are proposed that can detect change-points in the error distribution of nonparametric regression models. Different settings are considered where the change-point either occurs at some time point or at some value of the covariate. Fixed as well as random covariates are considered. Weak convergence of the suggested difference of sequential empirical processes based on nonparametrically estimated residuals to a Gaussian process is proved under the null hypothesis of no change point. In the case of testing for a change in the error distribution that occurs with increasing time in a model with random covariates the test statistic is asymptotically distribution-free and the asymptotic quantiles can be used for the test. This special test statistic can also detect a change in the regression function. In all other cases the asymptotic distribution depends on unknown features of the data generating process and a bootstrap procedure is proposed in these cases. The small sample performances of the proposed tests are investigated by means of a simulation study, and the tests are applied to a data example.
- Affiliations
Universität Hamburg Fachbereich Mathematik
Citations
Neumeyer, N., & Van Keilegom, I. (2006). Change-point tests for the error distribution in nonparametric regression (STAT Discussion Paper 0609). https://hdl.handle.net/2078.5/69016