Data-driven rate-optimal specification testing in regression models

• 成果类型: Article
• 署名作者: Guerre, E; Lavergne, P
• 署名单位: Sorbonne Universite; Universite PSL; Ecole des Hautes Etudes en Sciences Sociales (EHESS); Universite de Toulouse; Universite Toulouse 1 Capitole; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001200
• 发表日期: 2005
• 页码: 840-870
• 关键词: GOODNESS-OF-FIT; adaptive tests; bootstrap

摘要

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 I/root 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.