Non-asymptotic confidence intervals for importance sampling estimators of quantiles
Résumé
Building a confidence region (asymptotic or non-asymptotic) is crucial in understanding the quality of point estimators of a distribution. In this presentation, we estimate a quantile of a real random variable in the case where only a sample from another dominating distribution is available. This estimation procedure is known as importance sampling. A CLT is proved for the quantile estimator but the asymptotic variance depends on the true quantile, the unknown, and on its cumulative distribution function. We lift this barrier by building a non-asymptotic confidence interval for the true quantile which can be useful when only a limited sample size is available.
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