2005/05/30 by Emmanuel Guerre, Pascal Lavergne
Mathematics · #math.ST #stat.TH #msc:62G10 #msc:62G08.
paper · pdf · doi:10.1214/009053604000001200
published as Annals of Statistics 2005, Vol. 33, No. 2, 840-870 · 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)
arxiv created 2005/05/30 · arxiv updated 2009/12/01
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.