Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification
Annales de l'I.H.P. Probabilités et statistiques, Volume 18 (1982) no. 2, p. 149-163
@article{AIHPB_1982__18_2_149_0,
     author = {Duby, Camille and Rouault, Alain},
     title = {Estimation non param\'etrique de l'esp\'erance et de la variance de la loi de reproduction d'un processus de ramification},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {18},
     number = {2},
     year = {1982},
     pages = {149-163},
     zbl = {0484.62095},
     mrnumber = {662448},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPB_1982__18_2_149_0}
}
Duby, Camille; Rouault, Alain. Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification. Annales de l'I.H.P. Probabilités et statistiques, Volume 18 (1982) no. 2, pp. 149-163. http://www.numdam.org/item/AIHPB_1982__18_2_149_0/

[1] B.M. Brown, Martingale central limit theorems, Ann. Math. Stat., t. 42, 1971, p. 59-66. | MR 290428 | Zbl 0218.60048

[2] B.M. Brown, J.I. Hewitt, Inference for the diffusion branching process, J. A. P., t. 12, 1975, p. 588-594. | MR 378307 | Zbl 0313.60058

[3] J.P. Dion, Estimation des probabilités initiales et de la moyenne d'un processus de Galton-Watson. Thèse, Montréal, 1972.

[4] J.P. Dion, Estimation of the variance of a branching process. Ann. Stat., t. 3, 1975, p. 1183-1187. | MR 378308 | Zbl 0359.62067

[5] J. Dion, N. Keiding, Statistical inférence in branching processes, In Branching Processes edited by Joffe and Ney. Advances in Probability and Related Topics, t. 5, 1978, M. Dekker. | MR 517532 | Zbl 0405.62070

[6] C. Duby, A. Rouault, C. R. A. S., t. 290, 1980, p. 339-341. | MR 567763 | Zbl 0434.62064

[7] W. Eschenbach, W. Winkler, Maximum-likelihood-shätzungen beim Verzweigungsprozess von Galton-Watson. Math. Operations forsch. u. Stat., t. 6, 1975, p. 213-224. | MR 400585 | Zbl 0311.62055

[8] C.C. Heyde, On estimating the variance of the offspring distribution in a simple branching process, Adv. in Appl. Prob., t. 6, 1974, p. 421-433. | MR 348855 | Zbl 0305.60044

[9] C.C. Heyde, On an optimal asymptotic property of the maximum likelihood estimator of a parameter from a stochastic process. Stochastic Processes and their applications, t. 8, 1978, p. 1-9. | MR 511872 | Zbl 0387.62068

[10] C.C. Heyde, Some almost sure convergence theorems for branching processes, Z. Wahrscheinlichkeitstheorie, t. 20, 1971, p. 189-192. | MR 317426 | Zbl 0212.19703

[11] C.C. Heyde, B.M. Brown, An invariance principle and some convergence rate results for branching processes. Z. Wahrscheilichkeitstheorie, t. 20, 1971, p. 271-278. | MR 310987 | Zbl 0212.49505

[12] C.C. Heyde, P.D. Feigin, On efficiency and exponential families in stochastic process estimation. In : Statistical distributions in scientific work (ed. G. P. Patil, S. Kotz, J. K. Ord), Reidel, Dordrecht, t. 1, 1975, p. 227-240.

[13] P. Jagers, Branching processes with biological applications, Wiley, 1975. | Zbl 0356.60039

[14] N. Keiding, S. Lauritzen, Marginal maximum likelihood estimates and estimation of the offspring mean in a branching process. Scand. J. Statist., t. 5, 1978. | MR 497064 | Zbl 0378.62074

[15] Petrov, Sums of independent random variables, Springer-Verlag, 1975. | MR 388499 | Zbl 0322.60042

[16] Scott, A central limit theorem for martingales and an application to branching processes. Stochastic Processes and Their Applications, t. 6, 1978, p. 241-252. | MR 478301 | Zbl 0373.60023

[17] L. Weiss, J. Wolfowitz, Generalized maximum likelihood estimators. Theory of Prob. and its Appl., vol. XI, 1966, p. 58-80. | Zbl 0183.21202

[18] N.M. Yanev, On the statistics of branching processes. Theory of Prob. and its appl., t. 20, 1975, p. 612-622. | Zbl 0363.60073