On the asymptotic normality of finite population L-statistics

TL;DR

This paper establishes conditions under which finite population L-statistics, including trimmed means, are asymptotically normal in simple random samples without replacement, expanding understanding of their distributional properties.

Contribution

It provides new sufficient conditions for asymptotic normality of L-statistics, including a novel smoothness condition for trimmed means in finite populations.

Findings

Derived conditions for asymptotic normality of L-statistics.

Introduced a new smoothness condition for finite population trimmed means.

Extended the theoretical understanding of L-statistics in sampling contexts.

Abstract

We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of L-statistics. The second case is on trimmed means, where we introduce a new finite population smoothness condition.