On the Variance of Single-Run Unbiased Stochastic Derivative Estimators

Zhenyu Cui (), Michael C. Fu (), Jian-Qiang Hu (), Yanchu Liu (), Yijie Peng () and Lingjiong Zhu ()
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Zhenyu Cui: School of Business, Stevens Institute of Technology, Hoboken, New Jersey 07030
Michael C. Fu: The Robert H. Smith School of Business, Institute for Systems Research, University of Maryland, College Park, Maryland 20742
Jian-Qiang Hu: Department of Management Science, School of Management, Fudan University, Shanghai 200433, China
Yanchu Liu: Department of Finance, Lingnan (University) College, Sun Yat-sen University, Guangzhou, Guangdong 510275, China
Yijie Peng: Department of Management Science and Information Systems, Guanghua School of Management, Peking University, Beijing 100871, China
Lingjiong Zhu: Department of Mathematics, Florida State University, Tallahassee, Florida 32306

INFORMS Journal on Computing, 2020, vol. 32, issue 2, 390-407

Abstract: We analyze the variance of single-run unbiased stochastic derivative estimators. The distribution of a specific conditional expectation characterizes an intrinsic distributional property of the derivative estimators in a given class, which, in turn, separates two of the most popular single-run unbiased derivative estimators, infinitesimal perturbation analysis and the likelihood ratio method, into disjoint classes. In addition, a necessary and sufficient condition for the estimators to achieve the lowest variance in a certain class is provided, as well as insights into finding an estimator with lower variance. We offer a sufficient condition to substantiate the rule of thumb that the infinitesimal perturbation analysis estimator has a smaller variance than does the likelihood ratio method estimator and to provide a counterexample when the sufficient condition is not satisfied.

Keywords: simulation; stochastic derivative estimation; variance; infinitesimal perturbation analysis; likelihood ratio method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:32:y:2020:i:2:p:390-407

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