Pseudo-likelihood estimation for discretely observed multitype Bellman-Harris branching processes

Journal of Statistical Planning and Inference

Volumn 137, Issue 4, 2007, Pages 1375-1388

  Hyrien, Ollivier ^a  

^a UNIVERSITY OF ROCHESTER MEDICAL CENTER   (United States)

Author keywords

Branching process; Cell kinetics; Clonal data; Pure birth process; Quasi likelihood; Simulation based inference

Indexed keywords

EID: 33845209879     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2006.01.014     Document Type: Article

References (28)

1. Athreya K.B., and Keiding N. Estimation theory for continuous-time branching processes. Sankhya Ser. A 39 (1977) 101-123
2. Athreya K.B., and Ney P.E. Branching Processes (1972), Springer, Berlin
3. Bharucha-Reid A.T. Elements of the Theory of Markov Processes and their Applications (1960), McGraw-Hill, New York
4. Blum J.R. Multidimensional stochastic approximation methods. Ann. Math. Statist. 25 (1954) 737-744
5. Boucher K., Yakovlev A.Y., Mayer-Pröschel M., and Noble M. A stochastic model of temporarily regulated generation of oligodendrocytes in vitro. Math. Biosci. 159 (1999) 47-78
6. Boucher K., Zorin A., Yakovlev A.Y., Mayer-Pröschel M., and Noble M. An alternative stochastic model of generation of oligodendrocytes in cell culture. J. Math. Biol. 43 (2001) 22-36
7. von Collani E., Tsodikov A., Yakovlev A., Mayer-Pröschel M., and Noble M. A random walk model of oligodendrocyte generation in vitro and associated estimation problems. Math. Biosci. 159 (1999) 189
8. Concordet D., and Nuñez O. A simulated pseudo-maximum likelihood estimator for nonlinear mixed models. Comput. Statist. Data Anal. 39 2 (2002) 187-201
9. Dharmadhikari S.W., and Jogdeo K. Bounds on moments of certain random variables. Ann. Math. Statist. 40 (1969) 1506-1508
10. Gallant A.R., and White H. A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models (1988), Blackwell Scientific Publications Ltd, Oxford
11. Gourieroux C., and Monfort A. Simulation based inference in models with heterogeneity. Ann. Econom. Statist. 20/21 (1991) 69-107
12. Gourieroux C., Monfort A., and Trognon A. Pseudo maximum likelihood methods: theory. Econometrica 52 (1984) 681-700
13. Heyde C.C. Quasi-Likelihood and Its Applications. A General Approach to Optimal Parameter Estimation (1997), Springer, New York
14. Heyde, C.C., Lin, Y.X., 1992. On quasi-likelihood methods and estimation for branching process and heteroscedastic regression models. Australian Journal of Statistics 34, 199-206.
15. Hoel D.G., and Crump K.S. Estimating the generation-time distribution of an age-dependent branching process. Biometrics 30 (1974) 125-135
16. Hyrien O., Mayer-Pröschel M., Noble M., and Yakovlev A. A stochastic model to analyze clonal data on multi-type cell populations. Biometrics 61 (2005) 199-207
17. Hyrien O., Mayer-Pröschel M., Noble M., and Yakovlev A. Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture. Math. Biosci. 193 (2005) 255-274
18. Jennrich R.I. Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40 (1969) 633-643
19. Kiefer J., and Wolfowitz J. Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23 (1952) 462-466
20. Mode C.J. Multitype Branching Processes, Theory and Applications (1971), Elsevier, New York
21. Nedelman J., Downs H., and Pharr P. Inference on an age-dependent, multitype branching-process model of mast cells. J. Math. Biol. 25 (1985) 203-226
22. Nelder J.A., and Mead R. A simplex method for function minimization. Comput. J. 7 (1965) 308-313
23. Oh C., Severo N.C., and Slivka J. Approximations to the maximum likelihood estimate in some pure birth processes. Biometrika 78 (1991) 295-299
24. Sevast'yanov B.A. Branching Processes (1971), MIR, Moscow (in Russian)
25. Yakovlev A.Y., Boucher K., Mayer-Pröschel M., and Noble M. Quantitative insight into proliferation and differentiation of oligodendrocyte-type 2 astrocyte progenitor cells in vitro. Proc. Natl. Amer. Soc. USA 95 4 (1998) 14164-14167
26. Yakovlev A.Y., Mayer-Pröschel M., and Noble M. A stochastic model of brain cell differentiation in tissue culture. J. Math. Biol. 37 (1998) 49-60
27. Yakovlev A.Y., Mayer-Pröschel M., and Noble M. Stochastic formulations of a clock model for temporally regulated generation of oligodendrocytes in vitro. Math. Comput. Model. 32 (2000) 125-137
28. Zorin A.A., Yakovlev A.Y., Mayer-Pröschel M., and Noble M. Estimation problems associated with stochastic modeling of proliferation and differentiation of O-2A progenitor cells in vitro. Math. Biosci. 167 (2000) 109-121