Living on the Edge: An Unified Approach to Antithetic Sampling
Casarin, Roberto; Craiu, Radu V.; Frattarolo, Lorenzo; Robert, Christian (2022), Living on the Edge: An Unified Approach to Antithetic Sampling. https://basepub.dauphine.psl.eu/handle/123456789/24066
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Type
Document de travail / Working paperDate
2022Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
66
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Show full item recordAuthor(s)
Casarin, RobertoUniversité de Venise Ca’ Foscari | Università Ca’ Foscari di Venezia
Craiu, Radu V.
University of Toronto
Frattarolo, Lorenzo
European Commission Joint Research Centre (JRC), Ispra (VA), Italy
Robert, Christian
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We identify recurrent ingredients in the antithetic sampling literature leading to a unified sampling framework. We introduce a new class of antithetic schemes that includes the most used antithetic proposals. This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's τ and Spearman's ρ; iii)ranking in concordance order and iv) a central limit theorem that characterizes stochastic behavior of Monte Carlo estimators when the sample size tends to infinity. Finally, we provide applications to Monte Carlo integration and Markov Chain Monte Carlo Bayesian estimation.Subjects / Keywords
Antithetic variables; Countermonotonicity; Monte Carlo; Negativedependence; Variance reductionRelated items
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