Open Access
December 2007 Testing the suitability of polynomial models in errors-in-variables problems
Peter Hall, Yanyuan Ma
Ann. Statist. 35(6): 2620-2638 (December 2007). DOI: 10.1214/009053607000000361


A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used to estimate the distribution of the covariates under the null hypothesis, and a “wild” or moment-matching bootstrap argument is employed to estimate the distribution of the experimental errors (distinct from the distribution of the errors in covariates). Most of our attention is directed at the case where the distribution of the errors in covariates is known, although we also discuss methods for estimation and testing when the covariate error distribution is estimated. No assumptions are made about the distribution of experimental error, and, in particular, we depart substantially from conventional parametric models for errors-in-variables problems.


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Peter Hall. Yanyuan Ma. "Testing the suitability of polynomial models in errors-in-variables problems." Ann. Statist. 35 (6) 2620 - 2638, December 2007.


Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62042
MathSciNet: MR2382660
Digital Object Identifier: 10.1214/009053607000000361

Primary: 62G08 , 62G09 , 62G10 , 62G20

Keywords: bandwidth , bootstrap , Deconvolution , Distribution estimation , Hypothesis testing , Ill-posed problem , kernel methods , measurement error , moment-matching bootstrap , regularization , smoothing , wild bootstrap

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • December 2007
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