Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 2, pp. 289-319. 
@article{AIHPB_1993__29_2_289_0,
     author = {Johnstone, Iain M. and Macgibbon, K. Brenda},
     title = {Asymptotically minimax estimation of a constrained {Poisson} vector via polydisc transforms},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {289--319},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {2},
     year = {1993},
     mrnumber = {1227421},
     zbl = {0779.62022},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1993__29_2_289_0/}
}
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
SP  - 289
EP  - 319
VL  - 29
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1993__29_2_289_0/
LA  - en
ID  - AIHPB_1993__29_2_289_0
ER  - 
%0 Journal Article
%A Johnstone, Iain M.
%A Macgibbon, K. Brenda
%T Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1993
%P 289-319
%V 29
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1993__29_2_289_0/
%G en
%F AIHPB_1993__29_2_289_0
Johnstone, Iain M.; Macgibbon, K. Brenda. Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 2, pp. 289-319. http://www.numdam.org/item/AIHPB_1993__29_2_289_0/

J.O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd. ed., Springer Verlag, New York, 1985. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

L.D. Brown, An Heuristic Method for Determining Admissibility of Estimators - with Applications, Ann. Statist., Vol. 7, 1979, pp. 960-994. | MR | Zbl

M. Clevenson and J. Zidek, Simultaneous Estimation of the Mean of Independent Poisson Laws, J. Amer. Statist. Assoc., Vol. 70, 1975, pp. 698-705. | MR | Zbl

R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, 1953. | MR | Zbl

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. | MR | Zbl

D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin-Heidelberg, New York, 1983. | MR | Zbl

P.J. Huber, Robust Estimation of a Location Parameter, Ann. Math. Statist., 1964, Vol. 35, pp. 73-101. | MR | Zbl

P.J. Huber, Robust Statistics, Wiley, New York, 1981. | MR | Zbl

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. | Zbl

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. | Numdam | MR | Zbl

I.M. Johnstone and K.B. Macgibbon, Minimax Estimation of a Constrained Poisson Vector, Ann. Statist., Vol. 20, 1992, pp. 807-831. | MR | Zbl

O.A. Ladyzhenskaya and N.N. Ural'Tseva, Linear and Quasilinear Elliptic Equations, English translation, New York, Academic Press, 1968 (2nd. Russian edition, 1973). | MR | Zbl

B.Ya. Levit, On Asymptotic Minimax Estimates of the Second Order, Translation: Theor. Prob. Appl., Vol. 25, 1980, pp. 552-568. | Zbl

B.Ya. Levit, Minimax Estimation and Positive Solutions of Elliptic Equations, Translation: Theor. Prob. Appl., Vol. 27, 1982, pp. 563-586. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

M. Loève, Probability Theory I, Springer Verlag, New York, 1977. | MR | Zbl

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. | MR | Zbl

C. Miranda, Partial Differential Equations of Elliptic Type, 2nd. ed., Springer Verlag, New York, Heidelberg, 1970. | MR | Zbl

J.M. Steele, Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process, Ann. Prob., Vol. 14, 1986, pp. 326-335. | MR | Zbl