Boente, Graciela; Fraiman, Ricardo Robust nonparametric regression estimation for dependent observations. (English) Zbl 0683.62023 Ann. Stat. 17, No. 3, 1242-1256 (1989). 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. Cited in 1 ReviewCited in 33 Documents MSC: 62G05 Nonparametric estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:nonparametric regression; alpha-mixing; phi-mixing; autoregression; M- type robust equivariant estimators; kernel methods; k-nearest neighbor kernel methods; Strong consistency PDFBibTeX XMLCite \textit{G. Boente} and \textit{R. Fraiman}, Ann. Stat. 17, No. 3, 1242--1256 (1989; Zbl 0683.62023) Full Text: DOI