Asymptotic Properties of Empirical Quantile-Based Estimators by Martin Mugnier

Join us for this week's Econometrics Research Seminar, Spring Term 2025

Martin Mugnier, from the Paris School of Economics, will present this week's seminar on Asymptotic Properties of Empirical Quantile-Based Estimators.

Abstract

We consider the problem of inference on the mathematical expectation of unknown quantile-cdf transforms of a random variable. A prominent example is the Changes-in-Changes causal inference model developed by Athey and Imbens (2006, Econometrica), where the average treatment effect takes this form. Instead of relying on possibly restrictive differentiability conditions, bounded densities, and the functional delta method, we propose a novel large sample theory for a simple plug-in estimator. Our approach is based on weaker regularity assumptions, leveraging existing results from the theory of L-statistics and developing new results on the empirical process that may be of independent interest. Asymptotic normality is proven, and a new semiparametric estimator for the asymptotic variance is shown to be consistent under Hölder-type smoothness conditions on the densities. Monte Carlo simulations indicate that such sufficient conditions may also be necessary. Joint work with Julien Chhor (TSE), Xavier D’Haultfoeuille (CREST), and Jérémy L’Hour (CREST, Capital Fund Management).

This seminar will be held on campus, is open to all levels of study and is also open to the public. To register your place and gain access to the webinar, please contact the seminar organisers.

This event is part of the Econometrics Research Seminar Series.