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Non-Gaussian bifurcating models and quasi-likelihood estimation

Part of: Applications Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

I. V. Basawa  and
J. Zhou
I. V. Basawa
Affiliation:
Department of Statistics, University of Georgia, 101 Cedar Street, Athens, GA 30602-1952, USA. Email address: ishwar@stat.uga.edu
J. Zhou
Affiliation:
Department of Statistics, University of Georgia, 101 Cedar Street, Athens, GA 30602-1952, USA. Email address: jinzhou@stat.uga.edu
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Abstract

A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.

Keywords

Tree-indexed databifurcating autoregressive modelsmaximum likelihoodquasi-likelihood estimationMarkovian models

MSC classification

Primary: 62P10: Applications to biology and medical sciences
Secondary: 62M99: None of the above, but in this section
Type
Part 2. Estimation methods
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 55 - 64
Copyright
Copyright © Applied Probability Trust 2004 

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References

Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical Inference for Stochastic Processes. Academic Press, London.Google Scholar
Billingsley, P. (1961). Statistical Inference for Markov Processes. Chicago University Press.Google Scholar
Cowan, R. (1984). Statistical concepts in the analysis of cell lineage data. In Proc. 1983 Workshop Cell Growth Division , Latrobe University, Melbourne, pp. 18–22,Google Scholar
Cowan, R. and Staudte, R. G. (1986). The bifurcating autoregression model in cell lineage studies. Biometrics 42, 769–783.Google Scholar
Godambe, V. P. (1985). The foundations of finite sample estimation for stochastic processes. Biometrika 72, 419–428.Google Scholar
Grunwald, G. K., Hyndman, R. J., Tedesco, L. and Tweedie, R. L. (2000). Non-Gaussian conditional AR(1) models. Austral. N. Z. J. Statist. 42, 479–495.Google Scholar
Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. Academic Press, New York.Google Scholar
Heyde, C. C. (1997). Quasi-likelihood and Its Applications. Springer, New York.Google Scholar
Huggins, R. M. and Basawa, I. V. (1999). Extensions of the bifurcating autoregressive model for cell lineage studies. J. Appl. Prob. 36, 1225–1233.Google Scholar
Huggins, R. M. and Basawa, I. V. (2000). Inference for the extended bifurcating autoregressive model for cell lineage studies. Austral. N. Z. J. Statist. 42, 423–432.Google Scholar
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1997). Discrete Multivariate Distributions. John Wiley, New York.Google Scholar
Klimko, L. A. and Nelson, P. I. (1978). On conditional least squares estimation for stochastic processes. Ann. Statist. 6, 629–642.Google Scholar
Kotz, S., Balakrishnan, N. and Johnson, N. L. (2000). Continuous Multivariate Distributions , Vol. 1, Models and Applications , 2nd edn. John Wiley, New York.Google Scholar
Mardia, K. V. (1970). Families of Bivariate Distributions. Griffin, London.Google Scholar
Powell, E. O. (1955). Some features of the generation times of individual bacteria. Biometrika 42, 16–44.Google Scholar