Local linear regression estimation under long-range dependence: Strong consistency and rates

We consider the nonparametric estimation of multivariate regression functio ns and their derivatives for a regression model with long-range dependent e rrors. We adopt local linear fitting approach and establish strong consiste ncy and rates for the estimators of the regression function and its derivat ives. The rates of convergence depend on the amount of smoothing relative t o the strength of the long-range dependence (LRD) resulting in distinct rat es for small and large bandwidths. Moreover, the conditions determining thi s dichotomy are different for the estimates of the regression function than for the estimates of its derivatives.