A robust test for homoscedasticity in nonparametric regression

Holger Dette and Mareen Marchlewski

Journal of Nonparametric Statistics, 2010, vol. 22, issue 6, 723-736

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.

Date: 2010
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DOI: 10.1080/10485250903388894

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