Kernel density estimators for random fields satisfying an interlaced mixing condition

For a sequence of strictly stationary random fields that are uniformly ρ ′ - mixing and satisfy a Lindeberg condition, a central limit theorem is obtained for sequences of “rectangular” sums from the given random fields. The “Lindeberg CLT” is then used to prove a CLT for some kernel estimators of probability density for some strictly stationary random fields satisfying ρ ′ - mixing , and whose probability density and joint densities are absolutely continuous.