EURO 2024 Copenhagen
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4045. How to compute confidence intervals for quasi-Monte Carlo estimators

Invited abstract in session WD-6: Advancements of OR-analytics in statistics, machine learning and data science 19, stream Advancements of OR-analytics in statistics, machine learning and data science.

Wednesday, 14:30-16:00
Room: 1013 (building: 202)

Authors (first author is the speaker)

1. Pierre L'Ecuyer
DIRO, Université de Montréal
2. Marvin K. Nakayama
Computer Science, New Jersey Institute of Technology
3. Art B. Owen
Department of Statistics, Stanford University
4. Bruno Tuffin
Inria

Abstract

Randomized Quasi-Monte Carlo (RQMC) sampling provides unbiased estimators whose variance often converges at a faster rate than the standard Monte Carlo estimators as a function of the sample size n. But computing valid confidence intervals is not obvious because the n observations are dependent and the central limit theorem does not apply in general as n increases. A popular heuristic is to replicate the RQMC process r times (say, about 10) to obtain r independent realizations of the estimator, and use these r observations to compute a confidence interval based on the normal or Student distribution. Alternatives include various types of nonparametric bootstrap methods for which normality assumptions are not required. We report extensive numerical experiments that compare these methods in terms of the width and coverage probability of the confidence intervals, for a variety of examples. The results were not exactly as we expected. Based on these results, we give our recommendations.

Keywords

Status: accepted

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