期刊
JOURNAL OF NONPARAMETRIC STATISTICS
卷 15, 期 1, 页码 31-51出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10485250306038
关键词
conditional U-statistics; heteroscedasticity; ISE; Kernel estimators; L-2-test; nonparametric regression with random design; nonparametric variance estimators
We consider the nonparametric regression model with random design and derive an asymptotic alpha-test for testing the hypothesis that the conditional variance of the observations is constant against the alternative that it depends on the design. The test statistic is based on a L-2-distance between nonparametric variance estimators in both models-the underlying heteroscedastic model and in the hypothetical homoscedastic model. The proposed test is a consequence of a limit theorem for the weighted Integrated Square Error of nonparametric estimators of the conditional variance. Power considerations complete the approach.
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