M-estimation for the partially linear regression model under monotonic constraints

In this paper, we study M-estimation for the partially linear model under monotonic constraints. We use monotone B-splines to approximate the monotone nonparametric function. We show the large sample properties of the resulting estimators. The proposed estimator of parameter part is root-n consistent, and asymptotically normal and the estimator for the nonparametric component achieves the optimal convergence rate. A simulation study is conducted to evaluate the finite sample performance of the method. The proposed procedure is illustrated by an air pollution study.