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April 1998 Validation of linear regression models
Holger Dette, Axel Munk
Ann. Statist. 26(2): 778-800 (April 1998). DOI: 10.1214/aos/1028144860


A new test is proposed in order to verify that a regression function, say $g$, has a prescribed (linear) parametric form. This procedure is based on the large sample behavior of an empirical $L^2$-distance between $g$ and the subspace $U$ spanned by the regression functions to be verified. The asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the $L^2$-distance between the regression function $g$ and the model space $U$. Based on this result, a test is proposed for the hypothesis that "$g$ is not in a preassigned $L^2$-neighborhood of $U$," whichallows the "verification" of the model $U$ at a controlled type I error rate. The suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic. In particular, it does not require nonparametric estimators of the regression function and hence, the test does not depend on the subjective choice of smoothing parameters.


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Holger Dette. Axel Munk. "Validation of linear regression models." Ann. Statist. 26 (2) 778 - 800, April 1998.


Published: April 1998
First available in Project Euclid: 31 July 2002

zbMATH: 0930.62041
MathSciNet: MR1626016
Digital Object Identifier: 10.1214/aos/1028144860

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

Keywords: $L^2$-distance , equivalence of regression functions , Nonparametric model check , validation of goodness of fit

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 1998
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