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Monte Carlo maximum likelihood estimation for discretely observed diffusion processes
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Beskos, Alexandros, Papaspiliopoulos, Omiros and Roberts, Gareth O. (2009) Monte Carlo maximum likelihood estimation for discretely observed diffusion processes. Annals of statistics, Vol.37 (No.1). pp. 223-245. doi:10.1214/07-AOS550 ISSN 0090-5364.
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Official URL: http://dx.doi.org/10.1214/07-AOS550
Abstract
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models aid its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity conditions, the Monte Carlo MLE converges a.s. to the true MLE. For datasize n -> infinity, we show that the number of Monte Carlo iterations should be tuned as O (n(1/2)) and we demonstrate the consistency properties of the Monte Carlo MLE as an estimator of the true parameter value.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Annals of statistics | ||||
Publisher: | Inst Mathematical Statistics | ||||
ISSN: | 0090-5364 | ||||
Official Date: | February 2009 | ||||
Dates: |
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Volume: | Vol.37 | ||||
Number: | No.1 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 223-245 | ||||
DOI: | 10.1214/07-AOS550 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Greek State Scholarship's Foundation, Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | GR/S61577/01 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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