Abstrakt
Nonparametric regression approaches are flexible modeling tools in mod- ern 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 ap- proximation instead.
It is an effective alternative to more straightforward but rather slow plug-in techniques. In this paper we introduce a proper bootstrap algorithm for a robustified versions of the nonparametric estimates, so called M-smoothers, or M-estimates respectively.
We distinguish situations for homoscedastic and het- eroscedastic 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.