Exponential rates for kernal density estimation under association

Abstract

The estimation of density based on positive dependent samples has been studied recently with consistency and asymptotic normality results being obtained. In what concerns the characterization on decrease rates the results have been scarce. The article proves an exponential decrease rate for the kernel estimator of the density with an uniform version, over compact sets. The conditions assumed impose convenient decrease rates on the covariance structure of the sample. Some examples supposing exponential but also polynomial decrease rates on the covariances that fulfill our assumptions are presented in the last section.