Journal
INFORMS JOURNAL ON COMPUTING
Volume 34, Issue 3, Pages 1729-1748Publisher
INFORMS
DOI: 10.1287/ijoc.2021.1135
Keywords
density estimation; conditional Monte Carlo; quasi-Monte Carlo
Categories
Funding
- IVADO Research Grant
- Natural Sciences and Engineering Research Council of Canada [RGPIN-110050]
- Canada Research Chair
- Inria International Chair
- Spanish Ministry of Economy and Competitiveness [SEV-2017-0718, PID2019-104927GB-C22, PID2019-108111RBI00]
- Basque Government [BERC 2018e2021, ELKARTEK KK-2020/00049, EXP. 2019/00432]
- European Regional Development Fund, European Social Fund
- computing infrastructure of i2BASQUE academic network and IZOSGI SGIker of the Universidad del Pais Vasco
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Using conditional Monte Carlo, we can obtain a random conditional density that serves as an unbiased estimator of the true density. By taking the average of independent replications, we can achieve a faster convergence rate for the density estimator. Combining this new estimator with randomized quasi-Monte Carlo further improves the error and convergence rate.
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean in the sense that, for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of O(1/n). When the sample is generated from a simulation model and we have control over how this is done, we can do better. We examine an approach in which conditional Monte Carlo yields, under certain conditions, a random conditional density that is an unbiased estimator of the true density at any point. By averaging independent replications, we obtain a density estimator that converges at a faster rate than the usual ones. Moreover, combining this new type of estimator with randomized quasi-Monte Carlo to generate the samples typically brings a larger improvement on the error and convergence rate than for the usual estimators because the new estimator is smoother as a function of the underlying uniformrandom numbers.
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