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Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization

Schneider, Grant W
http://rave.ohiolink.edu/etdc/view?acc_num=osu1406912247

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Statistics.
Stochastic differential equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and maximize the likelihood function. While sequential Monte Carlo methods have allowed for the accurate evaluation of likelihoods at fixed parameter values, there is still a question of how to find the maximum likelihood estimate. In this dissertation we propose an efficient Gaussian-process-based method for exploring the parameter space using estimates of the likelihood from a sequential Monte Carlo sampler. Our method accounts for the inherent Monte Carlo variability of the estimated likelihood, and does not require knowledge of gradients. The procedure adds potential parameter values by maximizing the so-called expected improvement, leveraging the fact that the likelihood function is assumed to be smooth. Our simulations demonstrate that our method has significant computational and efficiency gains over existing grid- and gradient-based techniques. Our method is applied to modeling stock prices over the past ten years and compared to the most commonly used model.
Peter Craigmile, Ph.D. (Advisor)
Radu Herbei, Ph.D. (Advisor)
Laura Kubatko, Ph.D. (Committee Member)
137 p.
Statistics
Discretely sampled diffusions; Expected improvement; Gaussian process; Sequential Monte Carlo; Parameter estimation

Recommended Citations

Citations

  • Schneider, G. W. (2014). Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406912247

    APA Style (7th edition)

  • Schneider, Grant. Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1406912247.

    MLA Style (8th edition)

  • Schneider, Grant. "Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406912247

    Chicago Manual of Style (17th edition)

osu1406912247
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This open access ETD is published by The Ohio State University and OhioLINK.