NONPARAMETRIC SEQUENTIAL PREDICTION FOR STATIONARY PROCESSES

• 成果类型: Article
• 署名作者: Morvai, Gusztav; Weiss, Benjamin
• 署名单位: MTA-BME Stochastics Research Group; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP576
• 发表日期: 2011
• 页码: 1137-1160
• 关键词: ergodic time-series; universal schemes; large numbers; output; LAW

摘要

We study the problem of finding an universal estimation scheme h(n) : R(n) -> R, n = 1, 2,... which will satisfy limt(->infinity) l/t Sigma(t)(i=1)|h(i)(X(0), X(1)....,X(i-l)) -E(X(i)|X(0), X(1),....,X(i-1))|(p) = 0 a.s. for all real valued stationary and ergodic processes that are in L. We will construct a single such scheme for all 1 < p <= infinity, and show that for p = 1 mere integrability does not suffice but L log(+) L does.