EFFICIENCY OF EMPIRICAL ESTIMATORS FOR MARKOV-CHAINS

• 成果类型: Article
• 署名作者: GREENWOOD, PE; WEFELMEYER, W
• 署名单位: Universitat Siegen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324459
• 发表日期: 1995
• 页码: 132-143
• 关键词: stationary distribution; convolution theorem; models

摘要

Suppose we observe a uniformly ergodic Markov chain with unknown transition distribution. The empirical estimator for a linear functional of the (invariant) joint distribution of two successive observations is defined using the pairs of successive observations. Its efficiency is proved using a martingale approximation. As a corollary we show efficiency of the empirical joint distribution function in the sense of a functional convolution theorem.