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Discontinuities in robust nonparametric regression with α-mixing dependence

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  • Marie Hušková
  • Matúš Maciak

Abstract

The main idea of the paper is to introduce a robust regression estimation method under an α-mixing dependence assumption, staying free of any parametric model restrictions while also allowing for some sudden changes in the unknown regression function. The sudden changes in the model may correspond to discontinuity points (jumps) or higher order breaks (jumps in corresponding derivatives) as well. We firstly derive some important statistical properties for local polynomial M-smoother estimates and we will propose a statistical test to decide whether some given point of interest is significantly important for a change to occur or not. As the asymptotic distribution of the test statistic depends on quantities which are left unknown we also introduce a bootstrap algorithm which can be used to mimic the target distribution of interest. All necessary proofs are provided together with some experimental results from a simulation study and a real data example.

Suggested Citation

  • Marie Hušková & Matúš Maciak, 2017. "Discontinuities in robust nonparametric regression with α-mixing dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 447-475, April.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:447-475
    DOI: 10.1080/10485252.2017.1303061
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    References listed on IDEAS

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    1. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
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    5. Gao, Jiti & Gijbels, Irene & Van Bellegem, Sebastien, 2008. "Nonparametric simultaneous testing for structural breaks," Journal of Econometrics, Elsevier, vol. 143(1), pages 123-142, March.
    6. Shan Sun & Ching-Yuan Chiang, 1997. "Limiting behavior of the perturbed empirical distribution functions evaluated at U -statistics for strongly mixing sequences of random variables," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-18, January.
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    Cited by:

    1. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.

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