Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification

Camille Duby; Alain Rouault

Annales de l'I.H.P. Probabilités et statistiques (1982)

  • Volume: 18, Issue: 2, page 149-163
  • ISSN: 0246-0203

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Duby, Camille, and 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 18.2 (1982): 149-163. <http://eudml.org/doc/77182>.

@article{Duby1982,
author = {Duby, Camille, Rouault, Alain},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {mean; variance; offspring distribution of Galton-Watson process; log-likelihood; maximum likelihood estimators; approximate likelihood; consistent; asymptotically normal; asymptotically efficient},
language = {fre},
number = {2},
pages = {149-163},
publisher = {Gauthier-Villars},
title = {Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification},
url = {http://eudml.org/doc/77182},
volume = {18},
year = {1982},
}

TY - JOUR
AU - Duby, Camille
AU - Rouault, Alain
TI - Estimation non paramétrique de l'espérance et de la variance de la loi de reproduction d'un processus de ramification
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1982
PB - Gauthier-Villars
VL - 18
IS - 2
SP - 149
EP - 163
LA - fre
KW - mean; variance; offspring distribution of Galton-Watson process; log-likelihood; maximum likelihood estimators; approximate likelihood; consistent; asymptotically normal; asymptotically efficient
UR - http://eudml.org/doc/77182
ER -

References

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  2. [2] B.M. Brown, J.I. Hewitt, Inference for the diffusion branching process, J. A. P., t. 12, 1975, p. 588-594. Zbl0313.60058MR378307
  3. [3] J.P. Dion, Estimation des probabilités initiales et de la moyenne d'un processus de Galton-Watson. Thèse, Montréal, 1972. 
  4. [4] J.P. Dion, Estimation of the variance of a branching process. Ann. Stat., t. 3, 1975, p. 1183-1187. Zbl0359.62067MR378308
  5. [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. Zbl0405.62070MR517532
  6. [6] C. Duby, A. Rouault, C. R. A. S., t. 290, 1980, p. 339-341. Zbl0434.62064MR567763
  7. [7] W. Eschenbach, W. Winkler, Maximum-likelihood-shätzungen beim Verzweigungsprozess von Galton-Watson. Math. Operations forsch. u. Stat., t. 6, 1975, p. 213-224. Zbl0311.62055MR400585
  8. [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. Zbl0305.60044MR348855
  9. [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. Zbl0387.62068MR511872
  10. [10] C.C. Heyde, Some almost sure convergence theorems for branching processes, Z. Wahrscheinlichkeitstheorie, t. 20, 1971, p. 189-192. Zbl0212.19703MR317426
  11. [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. Zbl0212.49505MR310987
  12. [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. [13] P. Jagers, Branching processes with biological applications, Wiley, 1975. Zbl0356.60039
  14. [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. Zbl0378.62074MR497064
  15. [15] Petrov, Sums of independent random variables, Springer-Verlag, 1975. Zbl0322.60042MR388499
  16. [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. Zbl0373.60023MR478301
  17. [17] L. Weiss, J. Wolfowitz, Generalized maximum likelihood estimators. Theory of Prob. and its Appl., vol. XI, 1966, p. 58-80. Zbl0183.21202
  18. [18] N.M. Yanev, On the statistics of branching processes. Theory of Prob. and its appl., t. 20, 1975, p. 612-622. Zbl0363.60073

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