On Weak Convergence of Parameter Estimators of General Statistical Parametric Models

L. Vostrikova

Publications mathématiques et informatique de Rennes (1986)

  • Volume: 1986, Issue: 1, page 146-167

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Vostrikova, L.. "On Weak Convergence of Parameter Estimators of General Statistical Parametric Models." Publications mathématiques et informatique de Rennes 1986.1 (1986): 146-167. <http://eudml.org/doc/274410>.

@article{Vostrikova1986,
author = {Vostrikova, L.},
journal = {Publications mathématiques et informatique de Rennes},
keywords = {Hellinger process; jump measure; compensator of jump measure; Skorokhod space; general statistical parametric models; filtrations; likelihood ratio processes; weak convergence; Gaussian model; maximum likelihood estimators; Bayesian estimators},
language = {eng},
number = {1},
pages = {146-167},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {On Weak Convergence of Parameter Estimators of General Statistical Parametric Models},
url = {http://eudml.org/doc/274410},
volume = {1986},
year = {1986},
}

TY - JOUR
AU - Vostrikova, L.
TI - On Weak Convergence of Parameter Estimators of General Statistical Parametric Models
JO - Publications mathématiques et informatique de Rennes
PY - 1986
PB - Département de Mathématiques et Informatique, Université de Rennes
VL - 1986
IS - 1
SP - 146
EP - 167
LA - eng
KW - Hellinger process; jump measure; compensator of jump measure; Skorokhod space; general statistical parametric models; filtrations; likelihood ratio processes; weak convergence; Gaussian model; maximum likelihood estimators; Bayesian estimators
UR - http://eudml.org/doc/274410
ER -

References

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  1. [1] P. Billingsley. Convergence of probability measures. Wiley, 1968. Zbl0944.60003MR233396
  2. [2] I.A. Ibragimov, R.Z. Hasminskij. Asymptotic theory of estimation. Nauka, 1979 (in Russian). Zbl0467.62025MR545339
  3. [3] J. Jacod. Calcul stochastique et problèmes de martingales. Lecture Notes in Math.714, Springer -Verlag, 1979. Zbl0414.60053MR542115
  4. [4] J. Jacod. Processus de Hellinger, absolue continuité, contiguité. Séminaire de Probabilités, Rennes, 1983. MR863320
  5. [5] R. Liptser, A. Shiryayev. On the problem of " predictable criteria of contiguity. Probab. Theory and Math. Stat.Fourth USSR-Japan Symposium, Proceedings, 1982 Lecture Notes in Math., Springer-Verlag, 1021, 1983. Zbl0544.60044MR736006
  6. [6] R. Liptser, A. Shiryayev. On contiguity of probability measures corresponding to semimartingales, Analysis MathematicaeII (1985). p. 93-124 Zbl0591.60039MR803190
  7. [7] J. Memin, A.N. Shiryayev. Distance de Hellinger-Kakutani des lois correspondant à deux processus à accroissements indépendants: Critères d'absolue continuité et de singularité. Z. Wahrseinlinchkeitstheorie and Verw. Cebiete, 70 (1985), p.67-90. Zbl0569.60038MR795789
  8. [8] A.N. Shiryayev. Martingales : Recent Developments, Results and Applications. Internat. Stat. Rev.1981, 49, p. 199-233. Zbl0478.60062MR651472
  9. [9] L. Vostrikova. On criteria (cn)-consistency of estimators. Stochastics, 11 (1984), p.p. 265-290. Zbl0558.62029MR735390
  10. [10] L. Vostrikova. Functional limit theorems for the likelihood processes (to appear in Annales Universitatis Scientarium Budapestinenses de Rolando Eötvös nominatae.) 
  11. [11] L. Vostrikova. On a weak convergence of likelihood ratio processes of general statistical parametric models. Stochastics (submitted). Zbl0643.60029MR959115

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