Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-15T17:13:56.609Z Has data issue: false hasContentIssue false

Estimation of the parameters of a semi-Markov process from censored records

Published online by Cambridge University Press:  01 July 2016

M. E. Thompson*
Affiliation:
University of Waterloo
*
Postal address: Department of Statistics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Abstract

The estimation of the parameters of a discrete-time semi-Markov process is considered, when the data consist of records of a large number of individuals observed in a specified short period of time. Such a problem may arise in the modelling of intra-urban mobility. Methods of estimation of the parameters are suggested, and a numerical example discussed for the case when the observation period consists of three consecutive time points.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1981 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was completed while the author was on sabbatical at Imperial College, London, and was supported in part by a grant from the Canada Council.

References

Boudon, R. (1973) Mathematical Structures of Social Mobility. Jossey-Bass, San Francisco.Google Scholar
Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123187.Google Scholar
Çinlar, E. (1975) Markov renewal theory—a survey. Management Sci. 21, 727752.Google Scholar
Cox, D. R. (1972) Regression models and life tables. J. R. Statist. Soc. B 34, 187220.Google Scholar
Cox, D. R. (1975) Partial likelihood. Biometrika 62, 269276.Google Scholar
Gilbert, G. (1972) Two Markov models of neighbourhood housing turnover. Environment and Planning 4, 133146.CrossRefGoogle Scholar
Ginsberg, R. (1971) Semi-Markov processes and mobility. J. Math. Sociol. 1, 233262.Google Scholar
Henry, N. W. (1971) The retention model: a Markov chain with variable transition probabilities. J. Amer. Statist. Assoc. 66, 264267.Google Scholar
Lagakos, S. W., Sommer, C. J. and Zelen, M. (1978) Semi-Markov models for partially censored data. Biometrika 65, 311317.Google Scholar
Lévy, P. (1954) Processus semi-Markoviens. Proc. Internat. Congress Mathematicians (Amsterdam) 3, 416426.Google Scholar
McGinnis, R. (1968) A stochastic model of social mobility. Amer. Sociol. Rev. 33, 712721.Google Scholar
Pyke, R. A. (1961) Markov renewal processes: definition and preliminary properties. Ann. Math. Statist. 32, 12311242.Google Scholar
Smith, W. L. (1955) Regenerative stochastic processes. Proc. R. Soc. London A 232, 631.Google Scholar
Weiss, G. H. and Zelen, M. (1965) A semi-Markov model for clinical trials. J. Appl. Prob. 2, 269285.Google Scholar