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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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    1. Einmahl, J.H.J. & van Keilegom, I., 2008. "Specification tests in nonparametric regression," Other publications TiSEM 2c94c2d8-8305-4fb1-b47f-7, Tilburg University, School of Economics and Management.
    2. Cheng, Fuxia, 2002. "Consistency of error density and distribution function estimators in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 257-270, October.
    3. Einmahl, J.H.J. & van Keilegom, I., 2008. "Tests for independence in nonparametric regression," Other publications TiSEM 4356c520-d1d5-4156-b5b7-0, Tilburg University, School of Economics and Management.
    4. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Other publications TiSEM 0c6f2c43-aa7d-45c1-9d43-7, Tilburg University, School of Economics and Management.
    5. Beran, R.J. & Le Cam, L. & Millar, P.W., 1987. "Convergence of stochastic empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 159-168, October.
    6. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(1), pages 156-187, February.
    7. Atsushi Inoue, "undated". "Testing Change in Time Series," Computing in Economics and Finance 1997 7, Society for Computational Economics.
    8. Ferger, Dietmar & Stute, Winfried, 1992. "Convergence of changepoint estimators," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 345-351, September.
    9. Ogden, Todd & Parzen, Emanuel, 1996. "Data dependent wavelet thresholding in nonparametric regression with change-point applications," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 53-70, June.
    10. Oyet, Alwell J. & Sutradhar, Brajendra, 2003. "Testing variances in wavelet regression models," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 97-109, January.
    11. Dietmar Ferger, 1994. "On the power of nonparametric changepoint-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 277-292, December.
    12. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    13. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    14. Lee, Sangyeol & Na, Seongryong, 2004. "A nonparametric test for the change of the density function in strong mixing processes," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 25-34, January.
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    Cited by:

    1. Natalie Neumeyer & Leonie Selk, 2025. "Testing for changes in the error distribution in functional linear models," Statistical Papers, Springer, vol. 66(2), pages 1-17, February.
    2. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.
    3. Leonie Selk & Natalie Neumeyer, 2013. "Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 770-788, December.
    4. 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.
    5. 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).
    6. 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).
    7. 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.
    8. 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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