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dc.contributor.authorL'Ecuyer, P.
dc.contributor.authorPuchhammer, F.
dc.description.abstractEstimating 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.sponsorshipNSERC Discovery Grant, IVADO Grant, ERDF, ESF, EXP. 2019/00432en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectdensity estimationen_US
dc.subjectquasi-Monte Carloen_US
dc.subjectMonte Carloen_US
dc.subjectconditional Monte Carloen_US
dc.subjectlikelihood ratioen_US
dc.subjectkernel density estimatoren_US
dc.titleDensity Estimation by Monte Carlo and Quasi-Monte Carloen_US
dc.journal.titleMonte Carlo and Quasi-Monte Carlo Methods 2020en_US

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