Robust nonparametric regression estimation

BOENTE, GRACIELA; FRAIMAN, RICARDO

JOURNAL OF MULTIVARIATE ANALYSIS

Elsevier

Lugar: Amsterdam; Año: 1989 vol. 29 p. 180 - 198

0047-259X

In this paper we define a robust conditional location functional without requiring any moment condition. We apply the nonparametric proposals considered by C. Stone (Ann. Statist. 5 (1977), 595–645) to this functional equation in order to obtain strongly consistent, robust nonparametric estimates of the regression function. We give some examples by using nearest neighbor weights or weights based on kernel methods under no assumptions whatsoever on the probability measure of the vector (X,Y). We also derive strong convergence rates and the asymptotic distribution of the proposed estimates.