Kernel density estimators for random fields satisfying an interlaced mixing condition

Abstract

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.