CONTENTS 1. Introduction and summary....................5 2. A class of exponential families..............6 3. The estimation problem......................12 4. Solution of the statistical games.........17 5. Some special cases............................32 6. Concluding remark.............................33 References............................................35
J. O. Berger (1985), Statistical Decision Theory and Bayesian Analysis, Springer, Berlin, 2nd ed.
D. Bierlein (1968), The development of the concept of statistical decision theory, Europ. Meet. Amsterdam, Select. Statist. Papers 1, 27-35.
D. Bierlein (1967), Zur Einbeziehung der Erfahrung in spieltheoretische Modelle, Operations Res. Verf. 3, 29-54.
L. Chen, J. Eichenauer-Herrmann and J. Lehn (1990), Gamma-minimax estimation of a multivariate normal mean, Metrika 37, 1-6.
T. A. DeRouen and T. J. Mitchell (1974), A $G_1$-minimax estimator for a linear combination of binomial probabilities, J. Amer. Statist. Assoc. 69, 231-233.
P. Diaconis and D. Ylvisaker (1979), Conjugate priors for exponential families, Ann. Statist. 7, 269-281.
J. Eichenauer, J. Lehn and S. Rettig (1988), A gamma-minimax result in credibility theory, Insur. Math. Econ. 7, 49-57.
K. Fan (1953), Minimax theorems, Proc. Nat. Acad. Sci. U.S.A. 39, 42-47.
D. A. Jackson, T. M. O'Donovan, W. J. Zimmer and J. J. Deely (1970), $G_2$-minimax estimators in the exponential family, Biometrika 57, 439-443.
N. L. Johnson and S. Kotz (1970), Continuous Univariate Distributions -1, Houghton Mifflin, Boston.
J. Kindler (1981), Statistische Entscheidungsprobleme mit nichtkompaktem Aktionenraum, Manuscripta Math. 34, 255-263.
E. L. Lehmann (1983), Theory of Point Estimation, Wiley, New York.
C. N. Morris (1982), Natural exponential families with quadratic variance functions, Ann. Statist. 10, 65-80.
C. N. Morris (1983), Natural exponential families with quadratic variance functions: statistical theory, Ann. Statist. 11, 515-529.
M. Neumann (1977), Bemerkungen zum von Neumannschen Minimaxtheorem, Arch. Math. (Basel) 29, 96-105.
H. Robbins (1964), The empirical Bayes approach to statistical decision problems, Ann. Math. Statist. 35, 1-20.
F. J. Samaniego (1975), On T-minimax estimation, Amer. Statistician 29, 168-169.
D. L. Solomon (1972), Λ-minimax estimation of a multivariate location parameter, J. Amer. Statist. Assoc. 67, 641-646.
M. C. K. Tweedie (1967), A mean-square-error characterization of binomial-type distributions, Ann. Math. Statist. 38, 620-623.
A. Wald (1950), Statistical Decision Functions, Wiley, New York.
A. J. Weir (1973), Lebesgue Integration and Measure, Cambridge Univ. Press.