Large deviations for method-of-quantiles estimators of one-dimensional parameters
Valeria Bignozzi, Claudio Macci, Lea Petrella
TL;DR
This paper investigates the large deviation properties of method-of-quantiles estimators for one-dimensional parameters, providing theoretical insights and comparisons with method-of-moments estimators.
Contribution
It offers new large deviation results for method-of-quantiles estimators and discusses optimal quantile levels and convergence behavior.
Findings
Large deviation principles established for method-of-quantiles estimators
Optimal quantile levels identified for specific models
Comparison shows different convergence properties from method-of-moments estimators
Abstract
We consider method-of-quantiles estimators of unknown parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level lambda in (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 lambda and we compare the convergence of the method-of-quantiles and method-of-moments estimators.
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