Edgeworth expansions of suitably normalized sample mean statistics for atomic Markov chains

• 成果类型: Article
• 署名作者: Bertail, P; Clémençon, S
• 署名单位: Japan Science & Technology Agency (JST); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Nanterre; Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0360-0
• 发表日期: 2004
• 页码: 388-414
• 关键词: berry-esseen theorem; bootstrap; functionals; moment; sums

摘要

This paper is devoted to the problem of estimating functionals of type mu( f) = integral fd mu from observations drawn from a positive recurrent atomic Markov chain X = (X-n)(nis an element ofN) with stationary distribution mu. The properties of different estimators are studied. Beyond an accurate estimation of their bias, the estimation of their asymptotic variance is considered. We also show that the results of Malinovskii (1987) on the validity of the formal Edgeworth expansion for sample mean statistics of type T-n = n(-1) Sigma(i=1)(n) f (X-i) extend to their studentized versions, normalized by the asymptotic variance estimates we consider.