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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Bootstrapping Nonparametric M-Smoothers with Independent Error Terms
verfasst von : Matúš Maciak
Erschienen in: Nonparametric Statistics
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Abstract
On the one hand, nonparametric regression approaches are flexible modeling tools in modern statistics. On the other hand, the lack of any parameters makes these approaches more challenging when assessing some statistical inference in these models. This is crucial especially in situations when one needs to perform some statistical tests or to construct some confidence sets. In such cases, it is common to use a bootstrap approximation instead. It is an effective alternative to more straightforward but rather slow plug-in techniques. In this contribution, we introduce a proper bootstrap algorithm for a robustified version of the nonparametric estimates, the so-called M-smoothers or M-estimates, respectively. We distinguish situations for homoscedastic and heteroscedastic independent error terms, and we prove the consistency of the bootstrap approximation under both scenarios. Technical proofs are provided and the finite sample properties are investigated via a simulation study.