Bootstraping of \(M\)-smoothers. (English) Zbl 1356.62057

Summary: Asymptotic distribution of local polynomial \(M\)-smoothers depends on some unknown quantities. However, a knowledge of this distribution is crucial for a hypotheses testing problem in a change-point model. Instead of using some plug-in techniques, which provide a poor approximation, a bootstrap algorithm is proposed to approximate the unknown distribution and a proper justification of this algorithm is given. Finally, some results are illustrated through a proposed simulation study.


62G09 Nonparametric statistical resampling methods
62G10 Nonparametric hypothesis testing
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