TY - JOUR
T1 - Pathwise estimation of probability sensitivities through terminating or steady-state simulations
AU - Hong, L. Jeff
AU - Liu, Guangwu
PY - 2010/3
Y1 - 2010/3
N2 - A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous.In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57(1) 118-130]. We show that the estimator is consistent and follows a central limit theorem for simulation outputs from both terminating and steady-state simulations, and the optimal rate of convergence of the estimator is n?2/5 where n is the sample size. We further demonstrate how to use importance sampling to accelerate the rate of convergence of the estimator to n?1/2, which is the typical rate of convergence for statistical estimation. We illustrate the performances of our estimators and compare them to other well-known estimators through several examples. © 2010 INFORMS.
AB - A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous.In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57(1) 118-130]. We show that the estimator is consistent and follows a central limit theorem for simulation outputs from both terminating and steady-state simulations, and the optimal rate of convergence of the estimator is n?2/5 where n is the sample size. We further demonstrate how to use importance sampling to accelerate the rate of convergence of the estimator to n?1/2, which is the typical rate of convergence for statistical estimation. We illustrate the performances of our estimators and compare them to other well-known estimators through several examples. © 2010 INFORMS.
KW - Gradient estimation
KW - Perturbation analysis
KW - Probability function
KW - Stochastic simulation
UR - http://www.scopus.com/inward/record.url?scp=77951186786&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-77951186786&origin=recordpage
U2 - 10.1287/opre.1090.0739
DO - 10.1287/opre.1090.0739
M3 - 21_Publication in refereed journal
VL - 58
SP - 357
EP - 370
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 2
ER -