NONPARAMETRIC REGRESSION UNDER LONG-RANGE DEPENDENT NORMAL ERRORS

We consider the fixed-design regression model with long-range dependen t normal errors and show that the finite-dimensional distributions of the properly normalized Gasser-Muller and Priestley-Chao estimators of the regression function converge to those of a white noise process. F urthermore, the distributions of the suitably renormalized maximal dev iations over an increasingly finer grid converge to the Gumbel distrib ution. These results contrast with our previous findings for the corre sponding problem of estimating the marginal density of long-range depe ndent stationary sequences.