@article{AIHPB_2002__38_2_193_0, author = {Kor\'anyi, Adam and MacGibbon, K. Brenda}, title = {Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {193--206}, publisher = {Elsevier}, volume = {38}, number = {2}, year = {2002}, mrnumber = {1899110}, zbl = {1010.62009}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_2002__38_2_193_0/} }
TY - JOUR AU - Korányi, Adam AU - MacGibbon, K. Brenda TI - Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2002 SP - 193 EP - 206 VL - 38 IS - 2 PB - Elsevier UR - http://archive.numdam.org/item/AIHPB_2002__38_2_193_0/ LA - en ID - AIHPB_2002__38_2_193_0 ER -
%0 Journal Article %A Korányi, Adam %A MacGibbon, K. Brenda %T Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball %J Annales de l'I.H.P. Probabilités et statistiques %D 2002 %P 193-206 %V 38 %N 2 %I Elsevier %U http://archive.numdam.org/item/AIHPB_2002__38_2_193_0/ %G en %F AIHPB_2002__38_2_193_0
Korányi, Adam; MacGibbon, K. Brenda. Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 2, pp. 193-206. http://archive.numdam.org/item/AIHPB_2002__38_2_193_0/
[1] Spectres et groupes cristallographiques I: Domaines euclidiens, Inventiones Mathematicae 58 (1980) 179-199. | MR | Zbl
,[2] Spectres et groupes cristallographiques II: Domaines spheriques, Annales de l'Institut Fourier 30 (1980) 237-248. | Numdam | MR | Zbl
, ,[3] Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York, 1985. | MR | Zbl
,[4] Second-order asymptotically minimax estimates for the mean of a normal population, Problemy Peredachi Informatsii 16 (3) (1980) 60-79, Translation: Problems of Information Transmission (1981) 212-229. | Zbl
, ,[5] Minimax estimation of the mean of a normal distribution when the parameter space is restricted, Ann. Statist. 9 (1981) 1301-1309. | MR | Zbl
,[6] Éléments de mathématique, Fascicule XXXIV, Groupes et algèbres de Lie, Chapitres IV, V et VI, Hermann, Paris, 1969.
,[7] Statistical Decision Theory, Mimeographed Notes, Cornell University, Ithaca, NY, 1979.
,[8] Information inequalities for the Bayes risk, Ann. Statist. 18 (1990) 1578-1594. | MR | Zbl
, ,[9] Estimating a bounded normal mean, Ann. Statist. 9 (1981) 868-876. | MR | Zbl
, ,[10] Minimax risk over hyperrectangles and implications, Ann. Statist. 18 (1990) 1416-1437. | MR | Zbl
, , ,[11] The Bateman Manuscript Project, Higher Transcendental Functions (3 volumes), McGraw-Hill, New York, 1953-1955, (Erdélyi A. (Ed.)).
,[12] Mathematical Statistics, A Decision Theoretic Approach, Academic, New York, 1967. | MR | Zbl
,[13] Introduction to Partial Differential Equations, Princeton University Press, 1995. | MR | Zbl
,[14] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. | MR | Zbl
, ,[15] A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. Ec. Norm. Super. 4 (1971) 409-445. | Numdam | Zbl
,[16] Minimax estimation of a constrained Poisson vector, Ann. Statist. 20 (1992) 807-831. | MR | Zbl
, ,[17] Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms, Annales de l'Institut Henri Poincaré, Probabilité et Statistiques 29 (1993) 289-319. | Numdam | MR | Zbl
, ,[18] Numerical specification of discrete least favorable prior distributions, SIAM J. Sci. Statist. Comput. 8 (1987) 171-184. | MR | Zbl
,[19] On asymptotic minimax estimates of the second order, Theor. Probab. Appl. 25 (1980) 552-568, (Translation). | Zbl
,[20] Minimax estimation and positive solutions of elliptic equations, Theor. Probab. Appl. 27 (1982) 563-586, (Translation). | MR | Zbl
,[21] Second order asymptotic optimality and positive solutions of Schrödinger's equation, Theor. Probab. Appl. 30 (1985) 333-363, (Translation). | MR | Zbl
,[22] Evaluation of the minimax risk, in: Proc. Fourth International Vilnius Conf. Prob. Theory Math. Stat., Vilnius, Vol. 4, 1985, pp. 181-183.
,[23] On second order admissibility in simultaneous estimation, in: , (Eds.), Proc. 1st. World Congress Bernoulli Soc. Tashkent, USSR, VNU Sc. Press, Ultrecht, 1986. | MR | Zbl
,[24] The volume of a compact Lie Group, Inventiones Mathematicae 56 (1980) 93-95. | MR | Zbl
,[25] Order Restricted Statistical Inference, Wiley, New York, 1988. | MR | Zbl
, , ,[26] Confidence bounds for normal means under order restrictions, with applications to dose-response curves, toxicology experiments, and low-dose extrapolation, J. Amer. Statist. Assoc. 81 (1986) 186-195. | Zbl
,[27] Bounded domains which are isospectral but not congruent, Ann. Sci. Ec. Norm. Super. IV (15) (1982) 441-456. | Numdam | MR | Zbl
,[28] Reflection groups and the eigenvalue problems of vibrating membranes with mixed boundary conditions, Tohoku Math. J. II (36) (1984) 175-183. | MR | Zbl
,[29] Statistical Decision Functions, Wiley, New York, 1950. | MR | Zbl
,[30] A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1962. | JFM | MR
,[31] Minimaxschatzer für den Mittelwert υ einer normalverteilten Zufallgröße mit bekannter Varianz bei vorgegebener oberer und unterer Schranke für υ, Math. Operationsforsch. Statist. Ser. Statist. 12 (1981) 551-557. | Zbl
,