Rates of convergence of M-estimators for partly linear models involving time series

摘要

The asymptotic behaviour of M-estimators constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that the M-estimators of the vector of parameters are asymptotically normal and the M-estimators of the nonparametric component achieve the optimal convergence rates for nonparametric regression. Our asymptotic theory includes L_1-, L_2-, L_p-norm, and Huber estimators as special cases.