Data-driven rate-optimal specification testing in regression models

Details Data-driven rate-optimal specification testing in regression models Data-driven rate-optimal specification testing in regression models

2005-05-30

arxiv.org/abs/math/0505640v1

Annals of Statistics 2005, Vol. 33, No. 2, 840-870

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000001200 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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/\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.

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