  We prove the asymptotic normality of the kernel density estimator (introduced
by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly
mixing random fields. Our approach is based on the Lindeberg's method rather
than on Bernstein's small-block-large-block technique and coupling arguments
widely used in previous works on nonparametric estimation for spatial
processes. Our method allows us to consider only minimal conditions on the
bandwidth parameter and provides a simple criterion on the (non-uniform) strong
mixing coefficients which do not depend on the bandwith.
