L-Statistics with Smooth Weight Functions Jackknife Well.

Abstract : The behavior of linear combinations of order statistics (L-statistics) under jackknifing is discussed. The asymptotic behavior of a jackknifed L-statistic is produced, and the pseudo-value based variance estimate is shown to be consistent under moderate smoothness and a trimming condition of the weight function. The results extend easily to functions of L-statistics and thus answer a question posed in Miller (1974). Monte Carlo results support small-sample applicability of the large-sample results for the construction of approximate confidence intervals. (Author)