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September 2012 The convergence rate and asymptotic distribution of the bootstrap quantile variance estimator for importance sampling
Jingchen Liu, Xuan Yang
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Adv. in Appl. Probab. 44(3): 815-841 (September 2012). DOI: 10.1239/aap/1346955266

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).

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Jingchen Liu. Xuan Yang. "The convergence rate and asymptotic distribution of the bootstrap quantile variance estimator for importance sampling." Adv. in Appl. Probab. 44 (3) 815 - 841, September 2012. https://doi.org/10.1239/aap/1346955266

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 06101466
MathSciNet: MR3024611
Digital Object Identifier: 10.1239/aap/1346955266

Subjects:
Primary: 62F40
Secondary: 65C05

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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