Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series

Abstract

The estimation of the multivariate probability density functions f(x1, … , xd), d ≥ 1, of a stationary random process {Xi} using wavelet methods is considered. Uniform rates of almost sure convergence over compact subsets of Rd for densities in the Besov space Bspq are established for strongly mixing processes.