  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 has been shown to outperform
maximum likelihood estimation (MLE) 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. This approach is generally inefficient in larger samples. In
this paper, we show that, by properly choosing the number of L-moments and
weighting these accordingly, we are able to construct an estimator that
outperforms MLE 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. Monte Carlo
evidence shows our proposed approach is able to outperform (in a mean-squared
error sense) MLE in smaller samples, whilst working as well as it in larger
samples. We then consider extensions of our approach to conditional and
semiparametric models, and apply the latter to study expenditure patterns in a
ridesharing platform in Brazil.
