17 février 2021

Martin Mugnier (CREST, ENSAE, IP Paris)
Estimation of Parameters Defined as Expectation of Quantile-CDF Transforms With Application to Causal Inference

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Lieu : Salle 2L8

Résumé : Developing statistical methods to infer the causal impact of policies on a given outcome based on non-experimental data is a workhorse challenge in econom(etr)ics. I will start the talk by introducing Rubin (1974)’s causal model, the popular Difference-in-Difference (DiD) method and a nonlinear extension of it, the « Changes-in-Changes » method. ​In this extension, the parameter of interest, the average treatment effect (ATE), can be expressed as the difference between the expectation of some random variable (the outcome of the treated after treatment) and the expectation of an (unknown) quantile-CDF transform of another random variable (the outcome of the treated before treatment). A « Changes-in-Changes » estimator can be obtained by replacing expectations, quantile and CDF transforms by their empirical counterparts. I will present new results showing that asymptotic normality of such estimators holds under much weaker conditions that what is currently known. The proofs rely in particular on results on the standard empirical process and the theory of L-statistics. Finally, the finite sample behavior of the estimator is investigated through Monte-Carlo simulations. Joint work with Xavier D’Haultfœuille (CREST/ENSAE) and Jérémy L’Hour (CREST/Insee).

Estimation of Parameters Defined as Expectation of Quantile-CDF Transforms With Application to Causal Inference  Version PDF

Ovidiu Munteanu (U. of Connecticut)
Sobolev inequality and the topology at infinity of complete manifolds

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Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

Résumé : We study the number of ends of manifolds admitting a general Sobolev inequality and apply our results to obtain topological information for self-similar solutions of the Ricci flow and the Mean Curvature Flow. The method is based on a detailed analysis of positive solutions of a given Schrodinger equation on such manifolds.

Sobolev inequality and the topology at infinity of complete manifolds  Version PDF