Advances in Applied Probability

The convergence rate and asymptotic distribution of the bootstrap quantile variance estimator for importance sampling

Jingchen Liu and Xuan Yang

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Abstract

Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value at risk. The variance of the weighted sample quantile estimator is usually a difficult quantity to compute. In this paper we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles of weighted empirical distributions. Under regularity conditions, we show that the bootstrap variance estimator is asymptotically normal and has relative standard deviation of order O(n-1/4).

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 3 (2012), 815-841.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1346955266

Digital Object Identifier
doi:10.1239/aap/1346955266

Mathematical Reviews number (MathSciNet)
MR3024611

Zentralblatt MATH identifier
06101466

Subjects
Primary: 62F40: Bootstrap, jackknife and other resampling methods
Secondary: 65C05: Monte Carlo methods

Keywords
Weighted quantile bootstrap variance estimator importance sampling

Citation

Liu, Jingchen; Yang, Xuan. The convergence rate and asymptotic distribution of the bootstrap quantile variance estimator for importance sampling. Adv. in Appl. Probab. 44 (2012), no. 3, 815--841. doi:10.1239/aap/1346955266. https://projecteuclid.org/euclid.aap/1346955266


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