Robust nonparametric regression estimation for dependent observations

BOENTE, GRACIELA; FRAIMAN, RICARDO

ANNALS OF STATISTICS, THE

Institute of Mathematical Statistics

Año: 1989 vol. 17 p. 1242 - 1256

0090-5364

Robust nonparametric estimators for regression and autoregression are proposed for $\varphi$- 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.