🤖 AI Summary
This paper addresses the low finite-sample efficiency of L-moment estimation arising from fixing the number of L-moments equal to the number of parameters. We propose an adaptive scheme wherein the number of L-moments—and their associated weights—increases with sample size. We establish, for the first time, an asymptotic theoretical framework for L-moment order selection that grows with sample size, and introduce the Generalized L-Moment Estimator (GLME). GLME retains asymptotic efficiency while substantially improving small-sample accuracy. Monte Carlo simulations demonstrate that GLME achieves significantly lower mean squared error than maximum likelihood estimation (MLE) in small samples, and converges asymptotically to MLE’s efficiency. An empirical application to Brazilian ride-hailing expenditure data further confirms its robustness and practical utility. The core innovation lies in relaxing the conventional fixed-dimension L-moment matching constraint, thereby unifying finite-sample superiority with asymptotic optimality.
📝 Abstract
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.