We use local polynomial fitting to estimate the nonparametric M-regression
function for strongly mixing stationary processes
{(Yi,Xi)}. We establish a strong uniform consistency rate
for the Bahadur representation of estimators of the regression function and its
derivatives. These results are fundamental for statistical inference and for
applications that involve plugging in such estimators into other functionals
where some control over higher order terms are required. We apply our results
to the estimation of an additive M-regression model.Comment: 40 page