We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(<italic>Y</italic>, <italic>null</italic>)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are...

In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result as we show from inefficient estimation methods or technical...