On the multivariate kernel distribution estimator for distribution functions under association

摘要

In this note we consider the estimation of the multivariatedistribution function Fp of the p-dimensional marginalof a stationary associated sequence. We show, under certainregularity conditions, the almost sure consistency andcharacterize the asymptotic behavior of the MSE. We alsocharacterize the asymptotic optimal bandwidth. Under some strongerassumptions on the covariance this bandwidth rate is shown to bethe same as for the independent case.