Quantile sensitivity estimation for dependent sequences

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, a...

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Bibliographic Details
Published in:Journal of applied probability 2016-09, Vol.53 (3), p.715-732
Main Authors: Jiang, Guangxin, Fu, Michael C.
Format: Article
Language:English
Subjects:
Analytical estimating
Asymptotic methods
Asymptotic properties
Central limit theorem
Consistency
Consistent estimators
Cumulative distribution functions
Estimates
Estimation bias
Estimators
Mathematical sequences
Partial derivatives
Perturbation methods
Quantiles
Queuing
Random variables
Regenerative
Research Papers
Sensitivity analysis
Studies
Unbiased estimators
Citations: Items that this one cites
Online Access:Get full text
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Description
Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2016.36