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 loc al polynomial estimators of the regression function. We show the diffe rences between stationary random sequences and independent, identicall y distributed sequences. In this case, the computation of biases is hi ghly dependent on the underlying dependence structure, contrarily to t he classical Nadaraya-Watson estimator.