Open Access
April 2005 Data-driven rate-optimal specification testing in regression models
Emmanuel Guerre, Pascal Lavergne
Ann. Statist. 33(2): 840-870 (April 2005). DOI: 10.1214/009053604000001200


We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to $1/\sqrt{n}$. Asymptotic critical values come from the standard normal distribution and the bootstrap can be used in small samples. A general formalization allows one to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.


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Emmanuel Guerre. Pascal Lavergne. "Data-driven rate-optimal specification testing in regression models." Ann. Statist. 33 (2) 840 - 870, April 2005.


Published: April 2005
First available in Project Euclid: 26 May 2005

zbMATH: 1068.62055
MathSciNet: MR2163161
Digital Object Identifier: 10.1214/009053604000001200

Primary: 62G10
Secondary: 62G08

Keywords: Hypothesis testing , nonparametric adaptive tests , selection methods

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 2 • April 2005
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