Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 18 (1982) no. 2, pp. 149-163. 
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     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'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {149--163},
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     volume = {18},
     number = {2},
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     url = {http://archive.numdam.org/item/AIHPB_1982__18_2_149_0/}
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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'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 18 (1982) no. 2, pp. 149-163. http://archive.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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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

[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 | Zbl

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

[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 | Zbl

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

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