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The use of approximating models in Monte Carlo maximum likelihood estimation

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  • Kuk, Anthony Y. C.

Abstract

To obtain the likelihood of a non-Gaussian state-space model, Durbin and Koopman (1997, Biometrika, 84, 669-684) first calculate the likelihood under an approximating linear Gaussian model and then use Monte Carlo methods to estimate the necessary adjustment factor. We show that Durbin and Koopman's method is closely related to a method proposed by Geyer (1994, J. Roy. Statist. Soc. B 56, 261-274) for simulating the likelihood of a random-effects model and to a method proposed by Schall (1991, Biometrika, 78, 719-727) for approximating the maximum likelihood estimate of a generalised linear mixed model. A hybrid method is proposed for approximating the entire likelihood function as opposed to Durbin and Koopman's pointwise approximation. We also suggest an alternative class of approximating models based on conjugate latent process and apply it to approximate the likelihood of a time series model for count data.

Suggested Citation

  • Kuk, Anthony Y. C., 1999. "The use of approximating models in Monte Carlo maximum likelihood estimation," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 325-333, December.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:4:p:325-333
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    References listed on IDEAS

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    1. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    3. P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
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    Cited by:

    1. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
    2. Christian N. Brinch, 2008. "Simulated Maximum Likelihood using Tilted Importance Sampling," Discussion Papers 540, Statistics Norway, Research Department.

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