CIRM - Videos & books Library - Universal inference using the split likelihood ratio test

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Auteurs : Ramdas, Aaditya K. (Auteur de la conférence)
CIRM (Editeur )

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Résumé : We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood ratio statistic, that we call “the split likelihood ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model-misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid p-values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.

Mots-Clés : Irregular models; confidence sequences; maximum likelihood

Codes MSC :
62C05 - General considerations
62F03 - Hypothesis testing
62G10 - Nonparametric hypothesis testing
62L12 - Sequential estimation

Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/ramdas_universal.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-05_Ramdas.mp4

Informations sur la Rencontre

Nom de la Rencontre : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Organisateurs de la Rencontre : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Année de la rencontre : 2020
URL de la Rencontre : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19642303
Citer cette vidéo: Ramdas, Aaditya K. (2020). Universal inference using the split likelihood ratio test. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19642303
URI : http://dx.doi.org/10.24350/CIRM.V.19642303

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Bibliographie

WASSERMAN, Larry, RAMDAS, Aaditya, et BALAKRISHNAN, Sivaraman. Universal Inference Using the Split Likelihood Ratio Test. arXiv preprint arXiv:1912.11436, 2019. - https://arxiv.org/abs/1912.11436

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