DENSITY-ESTIMATION IN THE L-INFINITY NORM FOR DEPENDENT DATA WITH APPLICATIONS TO THE GIBBS SAMPLER

• 成果类型: Article
• 署名作者: YU, B
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349146
• 发表日期: 1993
• 页码: 711-735
• 关键词: uniform consistency; random-variables; SEQUENCES

摘要

This paper investigates the density estimation problem in the L(infinity) norm for dependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain beta-mixing (or absolutely regular) conditions. Moreover, for given beta-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.