Large deviations for method-of-quantiles estimators of one-dimensional parameters

We consider method-of-quantiles estimators of unknown one-dimensional parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level λ∈(0,1). The aim is to present large deviation results for these estimators as the sample size tends to infinity. We study in detail several examples; for specific models we discuss the choice of the optimal value of λ and we compare the convergence of the method-of-quantiles and method-of-moments estimators.