Confidence intervals for quantiles using sectioning when applying variance-reduction techniques

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Abstract

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.

Original languageEnglish (US)
Article number19
JournalACM Transactions on Modeling and Computer Simulation
Volume24
Issue number4
DOIs
StatePublished - Aug 1 2014

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computer Science Applications

Keywords

  • Control variates
  • Importance sampling
  • Quantile
  • Value-at-risk
  • Variance reduction

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