On local linear regression for strongly mixing random fields

We investigate the local linear kernel estimator of the regression function g of a stationary and strongly mixing real random field observed over a general subset of the lattice Zd. Assuming that g is differentiable with derivative g′, we provide a new criterion on the mixing coefficients for the consistency and the asymptotic normality of the estimators of g and g′ under mild conditions on the bandwidth parameter. Our results improve the work of Hallin et al. (2004) in several directions.