L-statistics for repeated measurements data with application to trimmed means, quantiles and tolerance intervals

Abstract

The L-statistics form an important class of estimators in nonparametric statistics. Its members include trimmed means and sample quantiles and functions thereof. This article is devoted to theory and applications of L-statistics for repeated measurements data, wherein the measurements on the same subject are dependent and the measurements from different subjects are independent. This article has three main goals: (a) Show that the L-statistics are asymptotically normal for repeated measurements data. (b) Present three statistical applications of this result, namely, location estimation using trimmed means, quantile estimation and construction of tolerance intervals. (c) Obtain a Bahadur representation for sample quantiles. These results are generalisations of similar results for independently and identically distributed data. The practical usefulness of these results is illustrated by analysing a real data-set involving measurement of systolic blood pressure. The properties of the proposed point and interval estimators are examined via simulation.

Keywords:

• Bahadur representation
• Hadamard derivative
• L-estimators
• nonparametric inference
• order statistics
• statistical functional
• weighted empirical process

Acknowledgements

The authors would like to thank the reviewers and the Associate Editor for providing thoughtful comments on this work. They have led to substantial improvements in this article.