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A robust test for homoscedasticity in nonparametric regression

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  • Holger Dette
  • Mareen Marchlewski

Abstract

We consider a nonparametric location scale model and propose a new test for homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function that vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n−1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some nonrobust tests for a constant scale function, which have recently been proposed in the literature.

Suggested Citation

  • Holger Dette & Mareen Marchlewski, 2010. "A robust test for homoscedasticity in nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 723-736.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:723-736
    DOI: 10.1080/10485250903388894
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    Cited by:

    1. Juan Carlos Pardo-Fernández & M. Dolores Jiménez-Gamero, 2019. "A model specification test for the variance function in nonparametric regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 387-410, September.
    2. Boente, Graciela & Pardo-Fernández, Juan Carlos, 2016. "Robust testing for superiority between two regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 151-168.
    3. Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2012. "Bandwidth choice for robust nonparametric scale function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1594-1608.

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