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Estimating parametric semi-Markov models from panel data using phase-type approximations

Titman, Andrew (2014) Estimating parametric semi-Markov models from panel data using phase-type approximations. Statistics and Computing, 24 (2). pp. 155-164. ISSN 0960-3174

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Abstract

Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.

Item Type: Article
Journal or Publication Title: Statistics and Computing
Uncontrolled Keywords: B-splines ; gamma distribution ; Hidden Markov model ; misclassification ; Panel data ; Phase-type distribution ; Semi-Markov ; Weibull
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 58810
Deposited By: ep_importer_pure
Deposited On: 03 Oct 2012 13:10
Refereed?: Yes
Published?: Published
Last Modified: 17 Feb 2014 09:09
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/58810

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