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

We consider the nonparametric estimation of multivariate regression functions and their derivatives for a regression model with long-range dependent errors. We adopt a local linear fitting approach and establish strong consistency and rates for the estimators of the regression function and its derivatives. The rates of convergence depend on the amount of smoothing relative to the strength of the long-range dependence (LRD) resulting in distinct rates for small and large bandwidths. Moreover, the conditions determining this dichotomy are different for the estimates of the regression function than for the estimates of its derivatives.