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December 1998 Nonparametric comparison of several regression functions: exact and asymptotic theory
Holger Dette, Axel Munk
Ann. Statist. 26(6): 2339-2368 (December 1998). DOI: 10.1214/aos/1024691474

Abstract

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.

Citation

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Holger Dette. Axel Munk. "Nonparametric comparison of several regression functions: exact and asymptotic theory." Ann. Statist. 26 (6) 2339 - 2368, December 1998. https://doi.org/10.1214/aos/1024691474

Information

Published: December 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0927.62040
MathSciNet: MR1700235
Digital Object Identifier: 10.1214/aos/1024691474

Subjects:
Primary: 62G05
Secondary: 62G07, 62G10, 62G30

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 1998
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