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On the Variance of Single-Run Unbiased Stochastic Derivative Estimators

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhenyu Cui & Michael C. Fu & Jian-Qiang Hu & Yanchu Liu & Yijie Peng & Lingjiong Zhu, 2020. "On the Variance of Single-Run Unbiased Stochastic Derivative Estimators," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 390-407, April.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:2:p:390-407
    DOI: 10.1287/ijoc.2019.0897
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    References listed on IDEAS

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