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On the use of time series representations of population models

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
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Abstract

Many population models which are far from stationarity can nevertheless be written in autoregressive format, perhaps with random coefficient. It is the thesis of this paper that procedures developed for stationary time series models are a useful guide to inferential results for population processes and may indeed be directly applicable. The illustrations concentrate on estimation of the matrix of mean vital rates in an age-structured population.

Keywords

AUTOREGRESSIONBRANCHING PROCESSPOPULATION MODELSEQUENTIAL CONTROL OR DESIGN MODELVITAL RATES
Type
Part 6—Allied Stochastic Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 345 - 353
Copyright
Copyright © 1986 Applied Probability Trust 

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References

[1] Anderson, B. D. O. and Moore, J. B. (1976) A matrix Kronecker lemma. Linear Algebra Appl. 15, 227–234.CrossRefGoogle Scholar
[2] Anderson, T. W. and Taylor, J. B. (1979) Strong consistency of least squares estimates in dynamic models. Ann. Statist. 7, 484–489.CrossRefGoogle Scholar
[3] Asmussen, S. and Keiding, N. (1978) Maringale central limit theorems and asymptotic estimation theory for multitype branching processes. Adv. Appl. Prob. 10, 109–129.CrossRefGoogle Scholar
[4] Athreya, K., B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
[5] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[6] Hall, P. and Heyde, C. C. (1980) Martingale Limit Theory and its Application. Academic Press, New York.Google Scholar
[7] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[8] Heyde, C. C. (1984) On inference for demographic projection of small populations. Proceedings of the Neyman-Kiefer Conference, Berkeley, CA, 1983 , ed. Olshen, R. Wadsworth and IMS, to appear.Google Scholar
[9] Heyde, C. C. and Cohen, J. E. (1985) Confidence intervals for demographic projections based on products of random matrices. Theoret. Popn Biol. 27.CrossRefGoogle Scholar
[10] Hoppe, F. M. (1976) Supercritical multitype branching processes. Ann. Prob. 4, 393–401.CrossRefGoogle Scholar
[11] Mode, C. J. (1971) Multitype Branching Processes. Elsevier, New York.Google Scholar
[12] Nicholls, D. F. and Quinn, B. G. (1982) Random Coefficient Autoregressive Models: An Introduction. Lecture Notes in Statistics 11, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[13] Quine, M. P. (1970) The multi-type Galton-Watson process with immigration. J. Appl. Prob. 7, 411–422.CrossRefGoogle Scholar
[14] Quine, M. P. and Durham, P. (1977) Estimation for multitype branching processes. J. Appl. Prob. 14, 829–835.CrossRefGoogle Scholar