Density Estimation in the L Norm for Dependent Data with Applications to theGibbs Sampler

摘要

This paper investigates the density estimation problem in the L-infinity norm fordependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain 13-mixing (or absolutely regular) conditions. Moreover, for given 13-mixing coefficients, bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients. The rates and the bounds obtained are not only for estimating the density but also for its derivatives. The results are then applied to give uniform convergence rates in problems associated with the Gibbs sampler. (AN).