Nonparametric M-estimation for right censored regression model with stationary ergodic data

The present paper deals with a nonparametric M-estimation for right censored regression model with stationary ergodic data. Defined as an implicit function, a kernel-type estimator of a family of robust regression is considered when the covariate takes its values in Rd (d≥1) and the data are sampled from a stationary ergodic process. The strong consistency (with rate) and the asymptotic distribution of the estimator are established under mild assumptions. Moreover, a usable confidence interval is provided which does not depend on any unknown quantity. Our results hold without any mixing condition and do not require the existence of marginal densities. A comparison study based on simulated data is also provided.