dc.contributor.author L'Ecuyer, P. dc.contributor.author Puchhammer, F. dc.date.accessioned 2021-09-07T20:07:25Z dc.date.available 2021-09-07T20:07:25Z dc.date.issued 2021 dc.identifier.uri http://hdl.handle.net/20.500.11824/1330 dc.description.abstract Estimating the density of a continuous random variable $X$ has been studied extensively in statistics, in the setting where $n$ independent observations of $X$ are given a priori and one wishes to estimate the density from that. Popular methods include histograms and kernel density estimators. In this review paper, we are interested instead in the situation where the observations are generated by Monte Carlo simulation from a model. Then, one can take advantage of variance reduction methods such as stratification, conditional Monte Carlo, and randomized quasi-Monte Carlo (RQMC), and obtain a more accurate density estimator than with standard Monte Carlo for a given computing budget. We discuss several ways of doing this, proposed in recent papers, with a focus on methods that exploit RQMC. A first idea is to directly combine RQMC with a standard kernel density estimator. Another one is to adapt a simulation-based derivative estimation method such as smoothed perturbation analysis or the likelihood ratio method to obtain a continuous estimator of the cumulative density function (CDF), whose derivative is an unbiased estimator of the density. This can then be combined with RQMC. We summarize recent theoretical results with these approaches and give numerical illustrations of how they improve the convergence of the mean square integrated error. en_US dc.description.sponsorship NSERC Discovery Grant, IVADO Grant, ERDF, ESF, EXP. 2019/00432 en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject density estimation en_US dc.subject quasi-Monte Carlo en_US dc.subject Monte Carlo en_US dc.subject conditional Monte Carlo en_US dc.subject likelihood ratio en_US dc.subject kernel density estimator en_US dc.title Density Estimation by Monte Carlo and Quasi-Monte Carlo en_US dc.type info:eu-repo/semantics/conferenceObject en_US dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.relation.projectID ES/2PE/PID2019-104927GB-C22 en_US dc.relation.projectID ES/2PE/PID2019-108111RB-I00 en_US dc.relation.projectID EUS/BERC/BERC.2018-2021 en_US dc.relation.projectID EUS/ELKARTEK en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Monte Carlo and Quasi-Monte Carlo Methods 2020 en_US
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España