Inference in parametric models with many L-moments
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L-moments are expected values of linear combinations of order statistics that provide robust alternatives to traditional moments. The estimation of parametric models by matching sample L-moments – a procedure known as “method of L-moments” – has been shown to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments to be used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, as to achieve an order condition for identification. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, we are able to construct an estimator that outperforms both MLE and the traditional L-moment approach in finite samples, and yet does not suffer from efficiency losses asymptotically. We do so by considering a “generalised” method of L-moments estimator and deriving its asymptotic properties in a framework where the number of L-moments varies with sample size. We then propose methods to automatically select the number of L-moments in a given sample. Monte Carlo evidence shows our proposed approach is able to outperform (in a mean-squared error sense) both the conventional L-moment approach and MLE in smaller samples, and works as well as MLE in larger samples.
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