Robust regression function estimation (Q793460)

An estimator of the regression function is proposed, which is a robust modification of the well-known kernel type estimator for the regression function. The robustification is in the spirit of Huber's theory of robust M-estimators of a location parameter. Strong and weak consistency and asymptotic normality are shown under rather weak conditions. The asymptotic variance is shown to be a product of a factor involving the kernel and a factor which relates to the asymptotic variance in a robust location problem. It is also shown that the estimation is minimax in the sense of \textit{P. J. Huber}, Ann. Math. Stat. 35, 73-101 (1964; Zbl 0136.398).