Testing for a constant coefficient of variation in nonparametric regression

Details Testing for a constant coefficient of variation in nonparametric regression Testing for a constant coefficient of variation in nonparametric regression

2008-09-29

arxiv.org/abs/0809.4937v1

Mathematics

Statistics Theory

29 pages

Scientific paper

In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function and variance function. We prove asymptotic normality of a standardized estimate of this distance under the null hypothesis and fixed alternatives and the finite sample properties of a corresponding bootstrap test are investigated by means of a simulation study. The results are applicable to stationary processes with the common mixing conditions and are used to construct tests for ARCH assumptions in financial time series.

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