ALMOST SURE CONVERGENCE OF CERTAIN SLOWLY CHANGING SYMMETRICAL ONE-SAMPLE AND MULTISAMPLE STATISTICS

• 成果类型: Article
• 署名作者: HENZE, N; VOIGT, B
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989819
• 发表日期: 1992
• 页码: 1086-1098
• 关键词: efron-stein inequality; nearest neighbor analysis; point-processes; jackknife estimate; variance; number

摘要

Let X(j)(i), i = 1,..., k; j is-an-element-of N, be independent d-dimensional random vectors which are identically distributed for each fixed i = 1,..., k. We give a sufficient condition for almost sure convergence of a sequence T(n1,...,n(k)) of statistics based on X(j)(i) i = 1,....k; j = 1,...,n(i), which are symmetric functions of X1(i),...,X(n(i))(i) for each i and do not change too much when variables are added or deleted. A key auxiliary tool for proofs is the Efron-Stein inequality. Applications include strong limits for certain nearest neighbor graph statistics, runs and empty blocks.