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Nonparametric analysis of covariance. (English) Zbl 1043.62033
Summary: In the problem of testing the equality of \(k\) regression curves from independent samples, we discuss three methods using nonparametric estimators of the regression function. The first test is based on a linear combination of estimators for the integrated variance function in the individual samples and in the combined sample. The second approach transfers the classical one-way analysis of variance to the situation of comparing nonparametric curves, while the third test compares the differences between the estimates of the individual regression functions by means of an \(L^2\)-distance.
We prove asymptotic normality of all considered statistics under the null hypothesis and local and fixed alternatives with different rates corresponding to the various cases. Additionally, consistency of a wild bootstrap version of the tests is established. In contrast to most of the procedures proposed in the literature, the methods introduced in this paper are also applicable in the case of different design points in each sample and heteroscedastic errors. A simulation study is conducted to investigate the finite sample properties of the new tests and a comparison with recently proposed and related procedures is performed.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G10 Nonparametric hypothesis testing
Software:
KernSmooth
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