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Nonparametric comparison of several regression functions: Exact and asymptotic theory. (English) Zbl 0927.62040
Summary: A new test is proposed for the comparison of two regression curves \(f\) and \(g\). We prove an asymptotic normal law under fixed alternatives which can be applied for power calculations, for constructing confidence regions and for testing precise hypotheses of a weighted \(L^2\) distance between \(f\) and \(g\). In particular, the problem of nonequal sample sizes is treated, which is related to a peculiar formula of the area between two step functions.
These results are extended in various directions, such as the comparison of \(k\) regression functions or the optimal allocation of the sample sizes when the total sample size is fixed. The proposed pivot statistic is not based on a nonparametric estimator of the regression curves and therefore does not require the specification of any smoothing parameter.

MSC:
62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
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