Estimateurs à rétrécisseurs de la moyenne d'une loi normale multidimensionnelle, pour un coût quadratique général

Dominique Cellier; Dominique Fourdrinier

Statistique et analyse des données (1985)

  • Volume: 10, Issue: 3, page 26-41
  • ISSN: 0750-7364

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Cellier, Dominique, and Fourdrinier, Dominique. "Estimateurs à rétrécisseurs de la moyenne d'une loi normale multidimensionnelle, pour un coût quadratique général." Statistique et analyse des données 10.3 (1985): 26-41. <http://eudml.org/doc/108929>.

@article{Cellier1985,
author = {Cellier, Dominique, Fourdrinier, Dominique},
journal = {Statistique et analyse des données},
keywords = {multivariate normal distribution; domination; generalized James-Stein estimators; shrinkage estimators; mean; maximum likelihood estimator; general quadratic loss},
language = {fre},
number = {3},
pages = {26-41},
publisher = {Association pour la statistique et ses illustrations},
title = {Estimateurs à rétrécisseurs de la moyenne d'une loi normale multidimensionnelle, pour un coût quadratique général},
url = {http://eudml.org/doc/108929},
volume = {10},
year = {1985},
}

TY - JOUR
AU - Cellier, Dominique
AU - Fourdrinier, Dominique
TI - Estimateurs à rétrécisseurs de la moyenne d'une loi normale multidimensionnelle, pour un coût quadratique général
JO - Statistique et analyse des données
PY - 1985
PB - Association pour la statistique et ses illustrations
VL - 10
IS - 3
SP - 26
EP - 41
LA - fre
KW - multivariate normal distribution; domination; generalized James-Stein estimators; shrinkage estimators; mean; maximum likelihood estimator; general quadratic loss
UR - http://eudml.org/doc/108929
ER -

References

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  1. [1] BEN MANSOUR, D., "Présentation, dans les cas classiques et bayésiens, des estimateurs de James-Stein généralisés", Thèse de 3 cycle de l'Université de Rouen, 1983. 
  2. [2] BERGER, J.O., "Minimax estimation of location vectors for a wide class of densities", The Annals of Statistics, 1975,Vol. 3, n°6, pp. 1318-1328. Zbl0322.62009MR386080
  3. [3] BERGER, J.O., "Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss", The Annals of Statistics, 1976, Vol. 4, n°l, pp. 223-226. Zbl0322.62007MR397940
  4. [4] BERGER, J.O., "Minimax estimation of a multivariate normal mean under arbitrary quadratic loss", Journal of Multivariate Analysis, 1976, 6, pp. 256-264. Zbl0338.62004MR408057
  5. [5] BERGER, J.O., "A robust generalized Bayes estimator and confidence region for a multivariate normal mean", The Annals of Statistics, 1980, Vol. 8, n°4, pp. 716-761. Zbl0464.62026MR572619
  6. [6] BERGER, J.O., BOCK, M.E., BROWN, L.D., CASELLA, G. and GLESER, L., "Minimax estimation of a normal mean vector for arbitrary quadratic loss and unknown covariance matrix", The Annals of Statistics, 1977, Vol. 5, n°4, pp. 763-771. Zbl0356.62009MR443156
  7. [7] BRANDWEIN, A.C., "Minimax estimation of the mean of spherically symmetric distribution under general quadratic loss", Journal of Multivariate Analysis, 1979, 9, pp. 579-588. Zbl0432.62033MR556913
  8. [8] BRANDWEIN, A.C. and STRAWDERMAN, W.E., "Minimax estimation of location parameters for spherically symmetric distributions with concave loss", The Annals of Statistics, 1980, Vol. 8, n°2, pp. 279-284. Zbl0432.62008MR560729
  9. [9] GLESER, L.J., "Minimax estimation of a normal mean vector when the covariance is unknown", The Annals of Statistics, 1979, Vol. 7, n°4, pp. 838-846. Zbl0418.62004MR532247
  10. [10] JAMES, W. and STEIN, C., "Estimation with quadratic loss", Proc. Fourth Berkeley Symp. Math. Statist. Prob., University of California Press, 1961, 1, pp. 361-379. Zbl1281.62026MR133191
  11. [11] JUDGE, G.G. and BOCK, M.E., The statistical implications of pretest and Stein rule estimators in econometrics, North-Holland, 1978. Zbl0395.62078MR483199
  12. [12] SCLOVE, S.L., MORRIS, C. and RADHAKRISHMAN, R., "Non-optimality of preliminary test estimators for the multinormal mean", The Annals of Mathematical Statistics, 1980, Vol. 43, n°5, pp. 1481-1490. Zbl0249.62029
  13. [13] SHINOZAKI, N., "Simultaneous estimation of location parameters under quadratic loss", The Annals of Statistics, 1984, Vol. 1, n°4, pp. 322-335. Zbl0542.62042MR733517
  14. [14] STEIN, C., "Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, Proc. Third Berkeley Symp. Math. Statist. Prob., University of California Press, 1955, 1, pp. 197-206. Zbl0073.35602MR84922
  15. [15] STEIN, C., "Estimation of the mean of a multivariate normal distribution", The Annals of Statistics, 1981, Vol. 9, n°6, pp. 1135-1151. Zbl0476.62035MR630098

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