L-moments are linear combinations of order statistics that provide robust alternatives to standard moments. The estimation of parametric density models by matching sample L-moments is known to outperform maximum likelihood estimation in small samples from several distributions. Recently, it has been further shown that, by varying the number of L-moments with sample size and weighting these acoordingly, one is able to construct an estimator that outperforms MLE in small samples, and yet does not underperform asymptotically. Methods to automatically select the number of L-moments have also been developed. Given their good statistical properties and computational simplicity, it is expected that extending L-moment-based approaches to estimation to semi- and nonparametric settings may be able to produce computationally convenient estimators with good statistical properties. In this paper, we undertake this task by extending the L-moment approach to the estimation of semiparametric models of treatment effects in randomised trials. Recently, Athey et al. (2021) introduced semiparametric models as a convenient tool for the analysis of experiments with heavy-tailed data. We show that, in their setting, a “plug-in” L-moment estimator produces an efficient estimator without requiring further corrections. For flexible parametrisations of treatment effects, our estimator is also computationally acttrative, as it can be obtained by solving a quadratic program. We also discuss how to perform specification testing and moment selection. As an application, we apply our methods to a randomised experiment conducted by a large car-hailing service in S˜ao Paulo, which randomised discounts to some of its active users. The goal of the experiment was to understand whether short-run changes in the prices of car rides starting or ending at train stations could lead to long-run changes in the demand for public transportation due to learning effects. For the largest discounts randomised, we observe large effects on bimodal rides during the weeks the discount was in place and no effects thereafter. As for unimodal (car-only) rides, we observe a negative effect after the discount is over, which persists over more than a month. We introduce a simple learning model that is able to rationalise these results.

Autores: Luis Antonio F. Alvarez e Ciro Biderman

Acesso o artigo aqui.