Minimum Hellinger distance estimation for supercritical Galton-Watson processes

Statistics and Probability Letters

Volumn 50, Issue 4, 2000, Pages 331-342

  Sriram, T N ^a   Vidyashankar, A N ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

60J80; 62F12; 62F35; Asymptotic efficiency* influence curves; Breakdown point; Hellinger functional; Minimum Hellinger distance

Indexed keywords

EID: 0042760476     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(00)00112-7     Document Type: Article

References (24)

1. Athreya K.B., Ney P.E. Branching Processes. 1972;Springer, Berlin.
2. Basawa I.V., Scott D.J. Efficient tests for branching processes. Biometrika. 63:1976;531-536.
3. Beran R.J. Minimum Hellinger distance estimates for parametric models. Ann. Statist. 5:1977;445-463.
4. Bhat B.R., Adke S.R. Maximum likelihood estimation for branching processes with immigration. Adv. Appl. Probab. 13:1981;498-509.
5. Billingsley P. Probability and Measure. 1979;Wiley, New York.
6. 1 View:1985;Wiley, New York.
7. Guttorp P. Statistical Inference for Branching Processes. 1991;Wiley, New York.
8. Györfi L., Vajda I., van der Meulen E. Minimum Hellinger distance point estimates consistent under weak family regularity. Math. Meth. Statist. 3:1994;25-45.
9. Hall P., Heyde C.C. Martingale Limit Theory and its Applications. 1980;Academic Press, New York.
10. Hampel, F.R., 1968. Contributions to the theory of robust estimation. Ph.D. Thesis, University of California, Berkeley.
11. Hampel F.R. A general qualitative definition of robustness. Ann. Math. Statist. 42:1971;1887-1896.
12. Heyde C.C., Brown B.M. An invariance principle and some convergence rate results for branching processes. Z. Wahrscheinlich-Keitsth. Verw. Geb. 20:1971;271-278.
13. Heyde C.C. Remarks on efficiency in estimation for branching processes. Biometrika. 62:1975;49-55.
14. Höpfner H., Kutoyants Y. On minimum distance estimation in recurrent Markov step processes. I. Scand. J. Statist. 61-79:1997.
15. Huber P.J. Robust statistics: a review. Ann. Math. Statist. 43:1972;1041-1067.
16. Huggins R.M. Variance - components models for dependent cell populations. J. Am. Statist. Assoc. 89:1994;19-29.
17. Huggins R.M. Robust inference for variance - components models for single trees of cell lineage data. Ann. Statist. 24:1996;1145-1160.
18. Koul H.L. Weighted Empiricals and Linear Models. IMS Lecture Notes. Vol. 21:1992;Hayward, California.
19. Podgorski, K., Vidyashankar, A.N., 1997. Minimum Hellinger distance estimation for stationary Markov chains - I. Unpublished Technical Report.
20. Simpson D.G. Minimum Hellinger distance estimation for the analysis of count data. J. Amer. Statist. Assoc. 82:1987;802-807.
21. Sriram, T.N., Vidyashankar, A.N., 1999. Minimum Hellinger distance estimation for supercritical Galton-Watson processes. Technical Report, Department of Statistics. The University of Georgia.
22. Staudte R.G. A bifurcating autoregression model for cell lineages with variable generation means. J. Theoret. Biol. 156:1992;183-195.
23. Staudte R.G., Huggins R.M., Zhang J., Axelrod D.E., Kimmel M. Estimating clonal heterogeneity and interexperiment variability with the bifurcating autoregressive model for cell lineage data. Math. Biol. Sci. 143:1997;103-121.
24. Sweeting T.J. On efficient tests for branching processes. Biometrika. 65:1978;123-128.