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.
| Original language | English |
|---|---|
| Pages (from-to) | 715-732 |
| Journal | Journal of Applied Probability |
| Volume | 53 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sept 2016 |
Funding
We thank the anonymous referee for useful comments and suggestions that have helped improve the paper. This work was supported in part by the National Science Foundation (NSF) under grants CMMI-0856256, CMMI-1362303, CMMI-1434419, and EECS-0901543, by the Air Force of Scientific Research (AFOSR) under grant FA9550-15-10050, and by the National Natural Science Foundation of China (project 11171256).
Research Keywords
- Quantile
- Monte Carlo simulation
- sensitivity analysis
- regenerative process
- phi-mixing
- REGENERATIVE SIMULATIONS
- PERTURBATION ANALYSIS
- STATIONARY