Inference on model parameters with many L-moments

TL;DR

This paper introduces a generalized L-moments estimation method that optimally chooses the number of L-moments, outperforming MLE in small samples while maintaining asymptotic efficiency, with applications to ridesharing data.

Contribution

It develops a new estimator that adaptively selects the number of L-moments, improving finite-sample performance over traditional methods.

Findings

Outperforms MLE in small samples in simulations

Retains asymptotic efficiency as sample size grows

Effective in estimating models for ridesharing expenditure data

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.