On the bias in local polynomial regression estimation for dependent data

In this Note, we give conditions in terms of the decay of the sequence of strong mixing coefficients in order to control the bias of the local polynomial estimators of the regression function. We show the differences between stationary random sequences and independent, identically distributed sequences. In this case, the computation of biases is highly dependent on the underlying dependence structure, contrarily to the classical Nadaraya-Watson estimator.