Approximating a sequence of observations by a simple process

• 成果类型: Article
• 署名作者: Rosenberg, D; Solan, E; Vieille, N
• 署名单位: Universite Paris 13; Northwestern University; Tel Aviv University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000643
• 发表日期: 2004
• 页码: 2742-2775
• 关键词: markov-chains; probabilistic functions; INEQUALITY; MODEL

摘要

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence. We generalize the result to the case where the one-step transitions are required to be in given polyhedra.