Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
Iain M. Johnstone; K. Brenda Macgibbon
Annales de l'I.H.P. Probabilités et statistiques (1993)
- Volume: 29, Issue: 2, page 289-319
- ISSN: 0246-0203
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topJohnstone, Iain M., and Macgibbon, K. Brenda. "Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms." Annales de l'I.H.P. Probabilités et statistiques 29.2 (1993): 289-319. <http://eudml.org/doc/77458>.
@article{Johnstone1993,
author = {Johnstone, Iain M., Macgibbon, K. Brenda},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {vector of independent Poisson variates; information normalized loss function; minimax risk; asymptotically minimax estimators; polydisk transform; principal eigenvalue; Laplace operator; -dimensional Poisson estimation; -dimensional Gaussian estimation},
language = {eng},
number = {2},
pages = {289-319},
publisher = {Gauthier-Villars},
title = {Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms},
url = {http://eudml.org/doc/77458},
volume = {29},
year = {1993},
}
TY - JOUR
AU - Johnstone, Iain M.
AU - Macgibbon, K. Brenda
TI - Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1993
PB - Gauthier-Villars
VL - 29
IS - 2
SP - 289
EP - 319
LA - eng
KW - vector of independent Poisson variates; information normalized loss function; minimax risk; asymptotically minimax estimators; polydisk transform; principal eigenvalue; Laplace operator; -dimensional Poisson estimation; -dimensional Gaussian estimation
UR - http://eudml.org/doc/77458
ER -
References
top- J.O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd. ed., Springer Verlag, New York, 1985. Zbl0572.62008MR804611
- P.E. Berkin and B.Ya. Levit, Second-Order Asymptotically Minimax Estimates for the Mean of a Normal Population, Problemy Peredachi Informatsii, Vol. 16, 3, 1980, pp. 60-79. Translation: Problems of Information Transmission, 1981, pp. 212-229. Zbl0466.62033MR624030
- P.J. Bickel, Minimax Estimation of the Mean of a Normal Distribution when the Parameter Space is Restricted, Ann. Statist., Vol. 9, 1981, pp. 1301-1309. Zbl0484.62013MR630112
- L.D. Brown, Admissible Estimators, Recurrent Diffusions and Insoluble Boundary Value Problems, Ann. Math. Statist., Vol. 42, 1971, pp. 855-903. Correction, Ann. Statist., Vol. 1, pp. 594-596. Zbl0246.62016MR286209
- L.D. Brown, An Heuristic Method for Determining Admissibility of Estimators - with Applications, Ann. Statist., Vol. 7, 1979, pp. 960-994. Zbl0414.62011MR536501
- M. Clevenson and J. Zidek, Simultaneous Estimation of the Mean of Independent Poisson Laws, J. Amer. Statist. Assoc., Vol. 70, 1975, pp. 698-705. Zbl0308.62018MR394962
- R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, 1953. Zbl0051.28802MR65391
- E.N. Dancer, The Effect of Domain Shape on the Number of Positive Solutions of Certain Nonlinear Equations, J. Diff. Eq., Vol. 74, 1988, pp. 120-156. Zbl0662.34025MR949628
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin-Heidelberg, New York, 1983. Zbl0562.35001MR737190
- P.J. Huber, Robust Estimation of a Location Parameter, Ann. Math. Statist., 1964, Vol. 35, pp. 73-101. Zbl0136.39805MR161415
- P.J. Huber, Robust Statistics, Wiley, New York, 1981. Zbl0536.62025MR606374
- I.M. Johnstone, Admissible Estimation, Dirichlet Principles and Recurrence of Birth-Death Chains on Zp+, Prob. Theory and Related Fields (= Z. Wahrsch. Th.), Vol. 71, 1986, pp. 213-269. Zbl0592.62009
- I.M. Johnstone and K.B. Macgibbon, Une mesure d'information caractérisant la loi de Poisson, Séminaire de Probabilités, Vol. XXI, 1987, pp.563-573, Lecture Notes in Mathematics, Vol. 1247, J. AZEMA, P. A. MEYER and M. YOR Eds., Springer Verlag, New York. Zbl0621.60028MR942005
- I.M. Johnstone and K.B. Macgibbon, Minimax Estimation of a Constrained Poisson Vector, Ann. Statist., Vol. 20, 1992, pp. 807-831. Zbl0761.62006MR1165594
- O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, English translation, New York, Academic Press, 1968 (2nd. Russian edition, 1973). Zbl0164.13002MR244627
- B.Ya. Levit, On Asymptotic Minimax Estimates of the Second Order, Translation: Theor. Prob. Appl., Vol. 25, 1980, pp. 552-568. Zbl0494.62035
- B.Ya. Levit, Minimax Estimation and Positive Solutions of Elliptic Equations, Translation: Theor. Prob. Appl., Vol. 27, 1982, pp. 563-586. Zbl0518.62031MR673924
- B.Ya. Levit, Second Order Asymptotic Optimality and Positive Solutions of Schrödinger's Equation, Translation: Theor. Prob. Appl., Vol. 30, 1985 a, pp. 333-363. Zbl0608.62035MR792622
- B.Ya. Levit, Evaluation of the Minimax Risk, Fourth International Vilnius Conf.Prob. Theory Math. Stat., Vol. 4, Vilnius, 1985 b, pp.181-183.
- B.Ya. Levit, On Second Order Admissibility in Simultaneous Estimation, Proc. 1st World Congress Bernouilli Soc. Tashkent, U.S.S.R., 1986, Yu. A. PROHOROV and V. V. SAZONOV Eds., V.N.U. Sc. Press, Utrecht. Zbl0686.62017MR1092458
- M. Loève, Probability Theory I, Springer Verlag, New York, 1977. Zbl0359.60001MR651017
- A.A. Melkman and Y. Ritov, Minimax Estimation of the Mean of a General Distribution when the Parameter Space is Restricted, Ann. Statist., Vol. 15, 1987, pp. 432-442. Zbl0621.62030MR885749
- C. Miranda, Partial Differential Equations of Elliptic Type, 2nd. ed., Springer Verlag, New York, Heidelberg, 1970. Zbl0198.14101MR284700
- J.M. Steele, Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process, Ann. Prob., Vol. 14, 1986, pp. 326-335. Zbl0592.60033MR815974
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