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Robust nonparametric regression estimation for dependent observations. (English) Zbl 0683.62023

Summary: Robust nonparametric estimators for regression and autoregression are proposed for \(\phi\)- and \(\alpha\)-mixing processes. Two families of M- type robust equivariant estimators are considered: (i) estimators based on kernel methods and (ii) estimators based on k-nearest neighbor kernel methods. Strong consistency of both families is proved under mild conditions. For the first class the result is true under no assumptions whatsoever on the distribution of the observations.

MSC:

62G05 Nonparametric estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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