Trimmed L-moments

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 in1uence on these methods. We de3ne 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 de3ned where the corresponding population L-moment does not exist: for example, the 3rst population TL-moment is well de3ned for a Cauchy distribution, but the 3rst population L-moment, the population mean, does not exist. The sample TL-mean is compared with other robust estimators of location. c © 2002 Elsevier Science B.V. All rights reserved.