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Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques MARVIN K. NAKAYAMA, New Jersey Institute of Technology We develop confidence intervals (CIs) for quantiles when applying variance-reduction techniques (VRTs) and sectioning. Similar to batching, sectioning partitions the independent and identically distributed (i.i.d.) outputs into nonoverlapping batches and computes a quantile estimator from each batch. But rather than centering the CI at the average of the quantile estimators across the batches, as in batching, sectioning centers the CI at the overall quantile estimator based on all the outputs. A similar modification is made to the sample variance, which is used to determine the width of the CI. We establish the asymptotic validity of the sectioning CI for importance sampling and control variates, and the proofs rely on first showing that the corresponding quantile estimators satisfy a Bahadur representation, which we have done in prior work. Here, we present some numerical results. Categories and Subject Descriptors: I.6.6 [Simulation and Modeling]: Simulation Output Analysis; G.3 [Probability and Statistics]: Nonparametric statistics; G.3 [Probability and Statistics]: Probabilistic algorithms (including Monte Carlo) General Terms: Performance, Theory Additional Key Words and Phrases: control variates, importance sampling, quantile, value-at-risk, variance reduction ACM Reference Format: Marvin http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1049-3301
DOI
10.1145/2558328
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Abstract

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques MARVIN K. NAKAYAMA, New Jersey Institute of Technology We develop confidence intervals (CIs) for quantiles when applying variance-reduction techniques (VRTs) and sectioning. Similar to batching, sectioning partitions the independent and identically distributed (i.i.d.) outputs into nonoverlapping batches and computes a quantile estimator from each batch. But rather than centering the CI at the average of the quantile estimators across the batches, as in batching, sectioning centers the CI at the overall quantile estimator based on all the outputs. A similar modification is made to the sample variance, which is used to determine the width of the CI. We establish the asymptotic validity of the sectioning CI for importance sampling and control variates, and the proofs rely on first showing that the corresponding quantile estimators satisfy a Bahadur representation, which we have done in prior work. Here, we present some numerical results. Categories and Subject Descriptors: I.6.6 [Simulation and Modeling]: Simulation Output Analysis; G.3 [Probability and Statistics]: Nonparametric statistics; G.3 [Probability and Statistics]: Probabilistic algorithms (including Monte Carlo) General Terms: Performance, Theory Additional Key Words and Phrases: control variates, importance sampling, quantile, value-at-risk, variance reduction ACM Reference Format: Marvin

Journal

ACM Transactions on Modeling and Computer Simulation (TOMACS) – Association for Computing Machinery

Published: May 1, 2014

References

  • A classified bibliography of research on stochastic PERT networks
    Adlakha V. G.