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Data-driven rate-optimal specification testing in regression models. (English) Zbl 1068.62055
Summary: 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 againts Pitman local alternatives approaching the parametric model at a rate arbitrarily close to \(1/\sqrt n\). Asymptotic critical values come from standard normal distributions 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.

MSC:
62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
62F03 Parametric hypothesis testing
62G09 Nonparametric statistical resampling methods
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