Free Access
Volume 18, 2014
Page(s) 365 - 399
Published online 03 October 2014
  1. V. Bansaye, Proliferating parasites in dividing cells: Kimmel’s branching model revisited. Ann. Appl. Probab. 18 (2008) 967–996. [CrossRef] [Google Scholar]
  2. I.V. Basawa and J. Zhou, Non-Gaussian bifurcating models and quasi-likelihood estimation. J. Appl. Probab. A 41 (2004) 55–64. [CrossRef] [Google Scholar]
  3. B. Bercu, B. de Saporta and A. Gégout-Petit, Asymptotic analysis for bifurcating autoregressive processes via a martingale approach. Electron. J. Probab. 14 (2009) 2492–2526. [MathSciNet] [Google Scholar]
  4. V. Blandin, Asymptotic results for bifurcating random coefficient autoregressive processes (2012). Preprint ArXiv: 1204.2926. [Google Scholar]
  5. A. Brandt, The stochastic equation Yn + 1 = AnYn + Bn with stationary coefficients. Adv. Appl. Probab. 18 (1986) 211–220. [CrossRef] [Google Scholar]
  6. Q.M. Bui and R.M. Huggins, Inference for the random coefficients bifurcating autoregressive model for cell lineage studies. J. Statist. Plann. Inference 81 (1999) 253–262. [CrossRef] [MathSciNet] [Google Scholar]
  7. R. Cowan and R.G. Staudte, The bifurcating autoregressive model in cell lineage studies. Biometrics 42 (1986) 769–783. [CrossRef] [PubMed] [Google Scholar]
  8. B. de Saporta, Tail of the stationary solution of the stochastic equation Yn + 1 = anYn + bn with Markovian coefficients. Stochastic Process. Appl. 115 (2005) 1954–1978. [CrossRef] [MathSciNet] [Google Scholar]
  9. B. de Saporta, A. Gégout-Petit and L. Marsalle, Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electron. J. Stat. 5 (2011) 1313–1353. [CrossRef] [Google Scholar]
  10. B. de Saporta, A. Gégout Petit and L. Marsalle, Asymmetry tests for bifurcating autoregressive processes with missing data. Stat. Probab. Lett. 82 (2012) 1439–1444. [CrossRef] [Google Scholar]
  11. J.-F. Delmas and L. Marsalle, Detection of cellular aging in a Galton-Watson process. Stoch. Process. Appl. 120 (2010) 2495–2519. [Google Scholar]
  12. M. Duflo, Random iterative models, Applications of Mathematics, vol. 34. Springer-Verlag, Berlin (1997). [Google Scholar]
  13. J. Guyon, Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann. Appl. Probab. 17 (2007) 1538–1569. [CrossRef] [Google Scholar]
  14. J. Guyon, A. Bize, G. Paul, E. Stewart, J.-F. Delmas and F. Taddéi, Statistical study of cellular aging, in CEMRACS 2004, mathematics and applications to biology and medicine, vol. 14, ESAIM: Proc. EDP Sci., Les Ulis (2005) 100–114 (electronic). [Google Scholar]
  15. P. Hall and C.C. Heyde, Martingale limit theory and its application. Probability and Mathematical Statistics. Academic Press Inc., New York (1980). [Google Scholar]
  16. J.D. Hamilton, Time series analysis. Princeton University Press, Princeton, NJ (1994). [Google Scholar]
  17. T.E. Harris, The theory of branching processes. Die Grundlehren der Mathematischen Wissenschaften, Bd. 119. Springer-Verlag, Berlin (1963). [Google Scholar]
  18. R.M. Huggins, Robust inference for variance components models for single trees of cell lineage data. Ann. Statist. 24 (1996) 1145–1160. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.M. Huggins and I.V. Basawa, Extensions of the bifurcating autoregressive model for cell lineage studies. J. Appl. Probab. 36 (1999) 1225–1233. [CrossRef] [Google Scholar]
  20. R.M. Huggins and I.V. Basawa, Inference for the extended bifurcating autoregressive model for cell lineage studies. Aust. N. Z. J. Stat. 42 (2000) 423–432. [CrossRef] [Google Scholar]
  21. R.M. Huggins and R.G. Staudte, Variance components models for dependent cell populations. J. AMS 89 (1994) 19–29. [Google Scholar]
  22. S.Y. Hwang and I.V. Basawa, Branching Markov processes and related asymptotics. J. Multivariate Anal. 100 (2009) 1155–1167. [Google Scholar]
  23. S.Y. Hwang and I.V. Basawa, Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality. J. Multivariate Anal. 102 (2011) 1018–1031. [CrossRef] [MathSciNet] [Google Scholar]
  24. Nicholls, D. F., and Quinn, B. G. Random coefficient autoregressive models: an introduction. In vol. 11, Lect. Notes Statist. Springer-Verlag, New York (1982). [Google Scholar]
  25. E. Stewart, R. Madden, G. Paul and F. Taddei, Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Biol. 3 (2005) e45. [Google Scholar]
  26. C.Z. Wei, Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. Ann. Statist. 15 (1987) 1667–1682. [CrossRef] [MathSciNet] [Google Scholar]
  27. J. Zhou and I.V. Basawa, Least-squares estimation for bifurcating autoregressive processes. Statist. Probab. Lett. 74 (2005) 77–88. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Zhou and I.V. Basawa, Maximum likelihood estimation for a first-order bifurcating autoregressive process with exponential errors. J. Time Ser. Anal. 26 (2005) 825–842. [CrossRef] [Google Scholar]

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