Trimmed L-moments

Elamir, Elsayed A.H.; Seheult, Allan H.

Abstract

Classical estimation methods (least squares, the method of moments and maximum likelihood) work well in regular cases such as the exponential family, but outliers can have undue influence on these methods. We define population trimmed L-moments (TL-moments) and corresponding sample TL-moments as robust generalisations of population and sample L-moments. TL-moments assign zero weight to extreme observations, they are easy to compute, their sample variances and covariances can be obtained in closed form, and they are more robust than L-moments are to the presence of outliers. Moreover, a population TL-moment may be well defined where the corresponding population L-moment does not exist: for example, the first population TL-moment is well defined for a Cauchy distribution, but the first population L-moment, the population mean, does not exist. The sample TL-mean is compared with other robust estimators of location.

Citation

Elamir, E. A., & Seheult, A. H. (2003). Trimmed L-moments. Computational Statistics & Data Analysis, 43(3), 299-314. https://doi.org/10.1016/s0167-9473%2802%2900250-5

• Journal Article Type: Article
• Publication Date: Jul 28, 2003
• Deposit Date: Feb 29, 2008
• Journal: Computational Statistics & Data Analysis
• Print ISSN: 0167-9473
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 3
• Pages: 299-314
• DOI: https://doi.org/10.1016/s0167-9473%2802%2900250-5
• Keywords: L-moments, Order statistics, Outliers, Robust estimation, Trimmed mean.