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 \textit{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. This approach is generally inefficient in larger sample sizes. 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 MLE 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) MLE in smaller samples, whilst working as well as it in larger samples.

翻译：L-矩是次序统计量线性组合的期望值，为传统矩提供了稳健的替代方案。通过匹配样本L-矩来估计参数模型（即“L-矩法”）已被证明在来自常用分布的小样本中优于最大似然估计（MLE）。然而，估计中所用L-矩数量的选择仍然是启发式的：研究人员通常将L-矩数量设置为与参数数量相等，以满足可识别性的阶条件。这种方法在较大样本量下通常效率低下。本文表明，通过合理选择L-矩数量并对其适当加权，我们能够构建一个在有限样本中优于MLE、且渐近效率无损失的估计量。为此，我们考虑一种“广义”L-矩法估计量，并在L-矩数量随样本量变化的框架下推导其渐近性质。随后，我们提出了在给定样本中自动选择L-矩数量的方法。蒙特卡洛证据显示，我们提出的方法在较小样本中能够（以均方误差衡量）优于MLE，同时在较大样本中表现与MLE相当。