DIFFERENTIABILITY OF STATISTICAL FUNCTIONALS AND CONSISTENCY OF THE JACKKNIFE

• 成果类型: Article
• 署名作者: SHAO, J
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349015
• 发表日期: 1993
• 页码: 61-75
• 关键词: frechet differentiability; likelihood

摘要

In statistical applications the unknown parameter of interest can frequently be defined as a functional theta = T(F), where F is an unknown population. Statistical inferences about 0 are usually made based on the statistic T(F(n)), where F(n) is the empirical distribution. Assessing T(F(n)) (as an estimator of theta) or making large sample inferences usually requires a consistent estimator of the asymptotic variance of T(F(n)). Asymptotic behaviour of the jackknife variance estimator is closely related to the smoothness of the functional T. This paper studies the smoothness of T through the differentiability of T and establishes some general results for the consistency of the jackknife variance estimators. The results are applied to some examples in which the statistics T(F(n)) are L-, M-estimators and some test statistics.