This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, which is inefficient in larger samples. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, one is able to construct an estimator that outperforms MLE in finite samples, and yet retains asymptotic efficiency. We do so by introducing a generalised method of L-moments estimator and deriving its properties in an asymptotic 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 sample. Monte Carlo evidence shows our approach can provide mean-squared-error improvements over MLE in smaller samples, whilst working as well as it in larger samples. We consider extensions of our approach to the estimation of conditional models and a class semiparametric models. We apply the latter to study expenditure patterns in a ridesharing platform in Brazil.

翻译：本文研究利用L-矩进行参数估计的方法，这是一种具有优越统计特性且可替代传统矩估计的技术。已知在常见分布的小样本中，通过匹配样本L-矩来估计模型参数的方法优于极大似然估计（MLE）。然而，估计中所用L-矩数量的选择仍缺乏系统准则：研究者通常将L-矩数量设为与参数个数相等，这在大样本中会导致效率损失。本文证明，通过合理选择L-矩数量并相应设置权重，可以构建在有限样本中优于MLE且保持渐近有效性的估计量。我们通过引入广义L-矩估计方法，并在L-矩数量随样本量变化的渐近框架下推导其性质来实现这一目标。随后提出自动选择样本中L-矩数量的方法。蒙特卡洛模拟表明，该方法在小样本中能提供优于MLE的均方误差改进，同时在大样本中保持与MLE相当的性能。我们将该方法拓展至条件模型和一类半参数模型的估计，并应用后者研究巴西某共享出行平台的消费行为模式。