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The use of approximating models in Monte Carlo maximum likelihood estimation

✍ Scribed by Anthony Y.C Kuk

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
102 KB
Volume
45
Category
Article
ISSN
0167-7152

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✦ Synopsis

To obtain the likelihood of a non-Gaussian state-space model, Durbin and Koopman (1997, Biometrika, 84, 669 -684) ΓΏrst 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-e ects 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.

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