Compatibility of multi-wave panel data and the continuous-time homogeneous Markov chain: An analysis of a continuous-time process by means of discrete-time longitudinal observations

Applied Stochastic Models and Data Analysis

Volumn 14, Issue 2-3, 1998, Pages 219-228

  Carette, Philippe ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Continuous time; Embedding problem; Markov chain; Panel data

Indexed keywords

DATA REDUCTION; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY;

CONTINUOUS TIME HOMOGENEOUS MARKOV CHAIN (CTHMC); PANEL DATA; TRANSITION PROBABILITY MATRIX;

MARKOV PROCESSES;

EID: 0032154839     PISSN: 87550024     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-0747(199809)14:3<219::aid-asm349>3.0.co;2-5     Document Type: Article

References (17)

1. J. S. Coleman, Introduction to Mathematical Sociology, The Free Press, New York 1964.
2. B. Singer and S. Spilerman, 'Fitting stochastic models to longitudinal survey data - some examples in the social sciences', Bull. Int. Statist. Inst., 47 (3), 283-300 (1977a).
3. B. Singer and J. E. Cohen, 'Malaria in Nigeria: constrained continuous-time Markov chains for discrete-time longitudinal data on human mixed-species infections', in Lecture on Mathematics in the Life Sciences, S. Levini (ed.), Vol. 12, American Mathematical Society, Providence, RI, 1979, pp. 69-133.
4. C. Hsiao, Analysis of Panel Data, Cambridge University Press, Cambridge, 1986.
5. M. Iosifescu, Finite Markov Processes and their Applications, Wiley, Chichester, 1980.
6. T. W. Anderson and L. A. Goodman, 'Statistical inference about Markov chains', Ann. Math. Stat., 28, 89-110 (1957).
7. J. H. Pollard, Numerical and Statistical Techniques, Cambridge University Press, Cambridge, 1977.
8. G. Elfving, 'Zur Theorie der Markoffschen Ketten', Acta Soc. Sci Fennicace n. Ser., A2 (8), (1937).
9. J. F. C. Kingman, 'The imbedding problem for finite Markov chains', Z. Wahrscheinlichkeitstheorie, 1, 14-24 (1962).
10. S. Johansen, 'Some results on the embedding problem for finite Markov chains', J. London Math. Soc. 8(2), 345-351 (1974).
11. P. Carette, 'Characterization of embeddable 3 × 3 stochastic matrices with a negative eigenvalue', New York J. Math., 1, 120-129 (1995)
12. P. Carette, New results on the embedding problem of homogeneous Markov chains with finitely many states, Ph.D. dissertation, Vrije Universiteit Brussel, 1997.
13. D. R. Cox and D. V. Hinkley, Theoretical Statistics, Chapman & Hall, London, 1974.
14. 2 tests', Biometrics, 10 (4), 417-451 (1954).
15. B. Fingleton, Models of Category Counts, Cambridge University Press, Cambidge 1984.
16. B. Singer and J. E. Cohen, 'Estimating malaria incidence and recovery rates from panel surveys', Math. Biosci., 49 (3-4), 273-305 (1980).
17. Y. W. W. Bishop, F. F. Fienberg and P. W. Holland, Discrete Multivariate Analysis', MIT Press, Cambridge, MA, 1975.