Randomized Quasi-Monte Carlo for Quantile Estimation

Document Type

Conference Proceeding

Publication Date

12-1-2019

Abstract

We compare two approaches for quantile estimation via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large but the size of the low-discrepancy point set remains fixed. In the first method, for each randomization, we compute an estimator of the cumulative distribution function (CDF), which is inverted to obtain a quantile estimator, and the overall quantile estimator is the sample average of the quantile estimators across randomizations. The second approach instead computes a single quantile estimator by inverting one CDF estimator across all randomizations. Because quantile estimators are generally biased, the first method leads to an estimator that does not converge to the true quantile as the number of randomizations goes to infinity. In contrast, the second estimator does, and we establish a central limit theorem for it. Numerical results further illustrate these points.

Identifier

85081138133 (Scopus)

ISBN

[9781728132839]

Publication Title

Proceedings Winter Simulation Conference

External Full Text Location

https://doi.org/10.1109/WSC40007.2019.9004679

ISSN

08917736

First Page

428

Last Page

439

Volume

2019-December

Grant

1537322

Fund Ref

National Science Foundation

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