Rates of uniform convergence for empirical processes of strictly stationaryβ-mixing sequences indexe

• 作 者: 张涤新
• 机 构: Department of Statistics
• 出 处: 中国科学A辑
• 发表日期: 2004年期
• 关键词: empirical processes unbounded index class β-mixing sequences convergence rates

Assume that {Xn} is a strictly stationary β-mixing random sequence with the β-mixing coefficient βk = O(k-r), 0 2 or p > 4, uniform convergence rates of empirical processes of strictly stationary β-mixing random sequence over the index classes can reach O((nr/(l+r)/logn)-1/2) or O((nr/(1+r)/ log n)-3/4) and that the Central Limit Theorem does not always hold for the empirical processes.``