![]() Petersburg Workshop on Simulation, 1996, pp. Glynn, Importance Sampling for Monte Carlo Estimation of Quantiles, Mathematical Methods in Stochastic Simulation and Experimental Design: Proceedings of the 2nd St. Shahabuddin, Variance reduction techniques for estimating value-at-risk, Management Sci. Nakayama, Quantile estimation with Latin hypercube sampling, Oper. Sloan, High-dimensional integration: the quasi-Monte Carlo way, Acta Numer. Discrepancy theory and quasi-Monte Carlo integration. Josef Dick and Friedrich Pillichshammer, Digital nets and sequences, Cambridge University Press, Cambridge, 2010.Owen, Consistency of Markov chain quasi-Monte Carlo on continuous state spaces, Ann. Bahadur, A note on quantiles in large samples, Ann. Wilson, Correlation-induction techniques for estimating quantiles in simulation experiments, Oper. We first prove the convergence of QMC-based quantile estimates under very mild conditions, and then establish a deterministic error bound of $O(N^)$ for arbitrarily small $\epsilon >0$. This paper focuses on the use of the quasi-Monte Carlo (QMC) method, whose convergence rate is asymptotically better than Monte Carlo in the numerical integration. Convergence analysis of quasi-Monte Carlo sampling for quantile and expected shortfallĪbstract: Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. ![]()
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