OPTIMAL STATISTIC BASED ON HIGHER-ORDER GAPS
成果类型：
Article
署名作者：
CRESSIE, N
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1979
页码：
619627
关键词：
摘要：
The family of statistics based on mth-order gaps from a uniform sample, obtained by summing a suitably regular function of each gap, is investigated. Holst (1979) established asymptotic normality together with explicit expressions for the mean and variance. This is extended to samples from distributions whose perturbations from uniformity shrink as sample size grows. From these results, Pitman asymptotic relative efficiencies can be calculated, and it is shown that the sum of squares of gaps is an optimal statistic. The properties of this statistic are presented, together with a comparison to the already well treated sum of log gaps. The 2 became indistinguishable as m, the order of the gaps, grows.