Trimmed L-moments

  • Authors:

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

  • Affiliations:

  • Department of Social Statistics, University of Southampton, Southampton S017 1BJ, UK;Science Laboratories, Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, UK

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2003

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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.