## The Annals of Statistics

### Robust Nonparametric Regression Estimation for Dependent Observations

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1242-1256.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347266

Digital Object Identifier
doi:10.1214/aos/1176347266

Mathematical Reviews number (MathSciNet)
MR1015148

Zentralblatt MATH identifier
0683.62023

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

#### Citation

Boente, Graciela; Fraiman, Ricardo. Robust Nonparametric Regression Estimation for Dependent Observations. Ann. Statist. 17 (1989), no. 3, 1242--1256. doi:10.1214/aos/1176347266. https://projecteuclid.org/euclid.aos/1176347266