Open Access
February 2009 Minimum distance regression model checking with Berkson measurement errors
Hira L. Koul, Weixing Song
Ann. Statist. 37(1): 132-156 (February 2009). DOI: 10.1214/07-AOS565


Lack-of-fit testing of a regression model with Berkson measurement error has not been discussed in the literature to date. To fill this void, we propose a class of tests based on minimized integrated square distances between a nonparametric regression function estimator and the parametric model being fitted. We prove asymptotic normality of these test statistics under the null hypothesis and that of the corresponding minimum distance estimators under minimal conditions on the model being fitted. We also prove consistency of the proposed tests against a class of fixed alternatives and obtain their asymptotic power against a class of local alternatives orthogonal to the null hypothesis. These latter results are new even when there is no measurement error. A simulation that is included shows very desirable finite sample behavior of the proposed inference procedures.


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Hira L. Koul. Weixing Song. "Minimum distance regression model checking with Berkson measurement errors." Ann. Statist. 37 (1) 132 - 156, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62028
MathSciNet: MR2400470
Digital Object Identifier: 10.1214/07-AOS565

Primary: 62G08
Secondary: 62G10

Keywords: consistency , Kernel estimator , L_2 distance , local alternatives

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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