Parameter Estimation for Multivariate Nonlinear Stochastic Differential Equation Models: A Comparison Study

Wei Gu, Hulin Wu () and Hongqi Xue ()
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Wei Gu: Zhongnan University of Economics and Law, School of Statistics and Mathematics
Hulin Wu: University of Texas Health Sciences Center
Hongqi Xue: University of Rochester, Department of Biostatistics and Computational Biology

A chapter in Statistical Modeling for Biological Systems, 2020, pp 245-258 from Springer

Abstract: Abstract Statistical methods have been proposed to estimate parameters in multivariate stochastic differential equations (SDEs) from discrete observations. In this paper, we propose a method to improve the performance of the local linearization method proposed by Shoji and Ozaki (Biometrika 85:240–243, 1998), i.e., to avoid the ill-conditioned problem in the computational algorithm. Simulation studies are performed to compare the new method to three other methods, the benchmark Euler method and methods due to Pedersen (1995) and to Hurn et al. (2003). Our results show that the new method performs the best when the sample size is large and the methods proposed by Pedersen and Hurn et al. perform better when the sample size is small. These results provide useful guidance for practitioners.

Keywords: Diffusion process; Euler–Maruyama scheme; Simulated maximum likelihood methods; Kernel density estimator; Local linearization method (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34675-1_13

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DOI: 10.1007/978-3-030-34675-1_13

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