Edgeworth approximations for distributions of symmetric statistics

• 成果类型: Article
• 署名作者: Bloznelis, Mindaugas; Goetze, Friedrich
• 署名单位: Vilnius University; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01144-x
• 发表日期: 2022
• 页码: 1153-1235
• 关键词: lattice point problems; expansion; VALUES; bounds

摘要

We study the distribution of a general class of asymptotically linear statistics which are symmetric functions of N independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a remainder of order o(N-1). The Edgeworth expansion is based on Hoeffding's decomposition which provides a stochastic expansion into a linear part, a quadratic part as well as smaller higher order parts. The validity of this Edgeworth expansion is proved under Cramer's condition on the linear part, moment assumptions for all parts of the statistic and an optimal dimensionality requirement for the non linear part.