Data-driven rate-optimal specification testing in regression models
Abstract
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/\sqrtn. 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.
Cite
@article{arxiv.math/0505640,
title = {Data-driven rate-optimal specification testing in regression models},
author = {Emmanuel Guerre and Pascal Lavergne},
journal= {arXiv preprint arXiv:math/0505640},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009053604000001200 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)