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Change‐Point Tests for the Error Distribution in Non‐parametric Regression

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  • NATALIE NEUMEYER
  • INGRID VAN KEILEGOM

Abstract

. Several testing procedures are proposed that can detect change‐points in the error distribution of non‐parametric 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 non‐parametrically 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.

Suggested Citation

  • Natalie Neumeyer & Ingrid Van Keilegom, 2009. "Change‐Point Tests for the Error Distribution in Non‐parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 518-541, September.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:518-541
    DOI: 10.1111/j.1467-9469.2009.00639.x
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    3. Markevičiūtė, J., 2016. "Epidemic change tests for the mean of innovations of an AR(1) process," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 79-91.
    4. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2014. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Discussion Papers ISBA 2014047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Marie Hušková & Zuzana Prášková, 2014. "Comments on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 265-269, June.
    7. Melanie Birke & Natalie Neumeyer, 2013. "Testing Monotonicity of Regression Functions – An Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 438-454, September.

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