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Quantile sensitivity estimation for dependent sequences

Part of: Multivariate analysis Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  24 October 2016

Guangxin Jiang  and
Michael C. Fu
Guangxin Jiang*
Affiliation:
City University of Hong Kong
Michael C. Fu*
Affiliation:
University of Maryland
*
*Postal address: Department of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong. Email address: [email protected]
** Postal address: Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.
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Abstract

In this paper we estimate quantile sensitivities for dependent sequences via infinitesimal perturbation analysis, and prove asymptotic unbiasedness, weak consistency, and a central limit theorem for the estimators under some mild conditions. Two common cases, the regenerative setting and ϕ-mixing, are analyzed further, and a new batched estimator is constructed based on regenerative cycles for regenerative processes. Two numerical examples, the G/G/1 queue and the Ornstein–Uhlenbeck process, are given to show the effectiveness of the estimator.

Keywords

QuantileMonte Carlo simulationsensitivity analysisregenerative processϕ-mixing

MSC classification

Primary: 62H12: Estimation
Secondary: 65C05: Monte Carlo methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 715 - 732
Copyright
Copyright © Applied Probability Trust 2016 

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