Quantile Estimation with Latin Hypercube Sampling

References

• Asmussen S, Glynn P (2007) Stochastic Simulation: Algorithms and Analysis (Springer, New York).Crossref, Google Scholar
• Avramidis AN, Wilson JR (1996) Correlation-induction techniques for estimating quantiles in simulation experiments. Technical Report NCSU-IE 95-5, North Carolina State University, Raleigh.Google Scholar
• Avramidis AN, Wilson JR (1998) Correlation-induction techniques for estimating quantiles in simulation. Oper. Res. 46(4):574–591.Link, Google Scholar
• Bahadur RR (1966) A note on quantiles in large samples. Ann. Math. Statist. 37(3):577–580.Crossref, Google Scholar
• Billingsley P (1995) Probability and Measure, 3rd ed. (John Wiley & Sons, New York).Google Scholar
• Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (John Wiley & Sons, New York).Crossref, Google Scholar
• Bloch DA, Gastwirth JL (1968) On a simple estimate of the reciprocal of the density function. Ann. Math. Statist. 39(3):1083–1085.Crossref, Google Scholar
• Bofinger E (1975) Estimation of a density function using order statistics. Australian J. Statist. 17(1):1–7.Crossref, Google Scholar
• Chu F, Nakayama MK (2012) Confidence intervals for quantiles when applying variance-reduction techniques. ACM Trans. Modeling Comput. Simulation 22(2):Article 10.Crossref, Google Scholar
• Dong H, Nakayama MK (2014) Constructing confidence intervals for a quantile using batching and sectioning when applying Latin hypercube sampling. Proc. 2014 Winter Simulation Conf. (IEEE, Piscataway, NJ), 640–651.Crossref, Google Scholar
• Falk M (1986) On the estimation of the quantile density function. Statist. Probab. Lett. 4(2):69–73.Crossref, Google Scholar
• Ghosh JK (1971) A new proof of the Bahadur representation of quantiles and an application. Ann. Math. Statist. 42(6):1957–1961.Crossref, Google Scholar
• Glasserman P (2004) Monte Carlo Methods in Financial Engineering (Springer, New York).Crossref, Google Scholar
• Glasserman P, Heidelberger P, Shahabuddin P (2000) Variance reduction techniques for estimating value-at-risk. Management Sci. 46(10):1349–1364.Link, Google Scholar
• Glynn PW (1996) Importance sampling for Monte Carlo estimation of quantiles. Proc. 2nd Internat. Workshop Math. Methods Stochastic Simulation Experiment. Design (Publishing House of St. Petersburg University, St. Petersburg, Russia), 180–185.Google Scholar
• Grabaskas D, Denning R, Aldemir T, Nakayama MK (2012) The use of Latin hypercube sampling for the efficient estimation of confidence intervals. Proc. 2012 Internat. Congress Adv. Nuclear Power Plants (ICAPP ’12) (American Nuclear Society, La Grange Park, IL), 1443–1452.Google Scholar
• Hall P, Martin MA (1988) Exact convergence rate of bootstrap quantile variance estimator. Probab. Theory Related Fields 80(2):261–268.Crossref, Google Scholar
• Hall P, Martin MA (1989) A note on the accuracy of bootstrap percentile method confidence intervals for a quantile. Statist. Probab. Lett. 8(3):197–200.Crossref, Google Scholar
• Hall P, Sheather SJ (1988) On the distribution of a Studentized quantile. J. Roy. Statist. Soc. Ser. B 50(3):381–391.Google Scholar
• Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engrg. System Safety 81(1):23–69.Crossref, Google Scholar
• Hesterberg TC, Nelson BL (1998) Control variates for probability and quantile estimation. Management Sci. 44(9):1295–1312.Link, Google Scholar
• Hsu JC, Nelson BL (1990) Control variates for quantile estimation. Management Sci. 36(7):835–851.Link, Google Scholar
• Jin X, Fu MC, Xiong X (2003) Probabilistic error bounds for simulation quantile estimation. Management Sci. 49(2):230–246.Link, Google Scholar
• Juneja S, Karandikar R, Shahabuddin P (2007) Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables. ACM Trans. Modeling Comput. Simulation 17(2):Article 2.Crossref, Google Scholar
• Kaczynski WH, Leemis LM, Drew JH (2012) Transient queueing analysis. INFORMS J. Comput. 24(1):10–28.Link, Google Scholar
• Liu J, Yang X (2012) The convergence rate and asymptotic distribution of bootstrap quantile variance estimator for importance sampling. Adv. Appl. Probab. 44(3):815–841.Crossref, Google Scholar
• Loh W-L (1996) On Latin hypercube sampling. Ann. Statist. 24(5):2058–2080.Crossref, Google Scholar
• McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting input variables in the analysis of output from a computer code. Technometrics 21(2):239–245.Google Scholar
• Nakayama MK (2011) Asymptotically valid confidence intervals for quantiles and values-at-risk when applying Latin hypercube sampling. Internat. J. Adv. Systems Measurements 4(1–2):86–94.Google Scholar
• Nakayama MK (2012) Confidence intervals for quantiles when applying replicated Latin hypercube sampling and sectioning. Nutaro J, Gay RJ, eds. Proc. Energy, Climate Environ. Modeling Simulation 2012 Conf. (ECEMS 2012), Autumn Simulation Multi-Conference, Vol. 44 (Society for Modeling and Simulation International, San Diego), 12–19.Google Scholar
• Nakayama MK (2014) Confidence intervals using sectioning for quantiles when applying variance-reduction techniques. ACM Trans. Modeling Comput. Simulation 24(4):Article 19.Crossref, Google Scholar
• Owen AB (1992) A central limit theorem for Latin hypercube sampling. J. Roy. Statist. Soc. Ser. B 54(2):541–551.Google Scholar
• Owen AB (1997) Monte Carlo variance of scrambled net quadrature. SIAM J. Numerical Anal. 34(5):1884–1910.Crossref, Google Scholar
• Serfling RJ (1980) Approximation Theorems of Mathematical Statistics (John Wiley & Sons, New York).Crossref, Google Scholar
• Stein M (1987) Large sample properties of simulations using Latin hypercube sampling. Technometrics 29(2):143–151. [Correction published 32(3):367.]Crossref, Google Scholar
• Sun L, Hong LJ (2010) Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk. Oper. Res. Lett. 38(4):246–251.Crossref, Google Scholar
• U.S. Nuclear Regulatory Commission (2010) Acceptance criteria for emergency core cooling systems for light-water nuclear power reactors. Title 10, Code of Federal Regulations Section 50.46, Nuclear Regulatory Commission, Washington, DC.Google Scholar
• U.S. Nuclear Regulatory Commission (2011) Applying statistics. U.S. Nuclear Regulatory Commission Report NUREG-1475, Rev. 1, U.S. Nuclear Regulatory Commission, Washington, DC.Google Scholar
• Williams D (1991) Probability with Martingales (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar