Inference in parametric models with many L-moments - Alvarez, Luís Antonio Fantozzi (2022)
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 in small samples from popular distributions. The choice of the number of L-moments to be used in estimation remains 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. In this thesis, we show that, by properly choosing the number of L-moments and weighting these accordingly, we are able to construct an estimator that outperforms both MLE and the traditional L-moment approach 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. As an extension, we show that a modification of our approach can be be used in the estimation of semiparametric models of treatment effects in randomised controlled trials (RCTs). This extension produces an efficient estimator with attractive computational properties. We illustrate the usefulness of our approach by applying it to data on an RCT conducted in São Paulo, Brazil. With such extension, we hope more generally to introduce L-moment-based estimation as an attractive procedure in settings where semi- and nonparametric maximum likelihood estimation is computationally complicated.