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

  • Wei Gu
  • Hulin WuEmail author
  • Hongqi Xue


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.


Diffusion process Euler–Maruyama scheme Simulated maximum likelihood methods Kernel density estimator Local linearization method 



This research was supported by the NIAID/NIH grants HHSN272201000055C and AI087135, and by two University of Rochester CTSI (UL1RR024160) pilot awards from the National Center for Research Resources of NIH.


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Authors and Affiliations

  1. 1.School of Statistics and MathematicsZhongnan University of Economics and LawWuhanPeople’s Republic of China
  2. 2.University of Texas Health Sciences CenterHoustonUSA
  3. 3.Department of Biostatistics and Computational BiologyUniversity of RochesterNew YorkUSA

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