References
Baranchik, A. J. (1973). Inadmissibility of maximum likelihood estimators in some multiple regression problems with three or more independent variables,Ann. Statist.,1, 312–321.
Basu, D. (1955). On statistics independent of a complete sufficient statistics,Sankhyã,15, 377–380.
Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testing from an exponential distribution.Ann. Math. Statist.,25, 373–381.
Ferguson, T. S. (1967).Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York.
Giri, N. C. (1977).Multivariate Statistical Inference, Academic Press, New York.
Hall, W. J., Wijsman, R. A. and Ghosh, J. K. (1965). The relationship between sufficiency and invariance with application in sequential analysis,Ann. Math. Statist.,36, 575–614.
Hora, R. B. and Buehler, R. J. (1967). Fiducial theory and invariant prediction,Ann. Math. Statist.,38, 795–801.
Ishii, G. (1969). Optimality of unbiased predictors,Ann. Inst. Statist. Math.,21, 471–488.
Nabeya, S. (1978).Mathematical Statistics (in Japanese), Kyöritu Press, Tokyö.
Skibinsky, M. (1967). Adequate subfields and sufficiency,Ann. Math. Statist.,38, 155–161.
Stein, C. (1960). Multiple regression,Contribution to Probability and Statistics, Stanford Univ. Press.
Sugiura, M. and Morimoto, H. (1969). Factorization theorem for adequate σ-field (in Japanese),Sügaku,21, 286–289.
Takada, Y. (1979). A family of minimax estimators in some multiple regression problems,Ann. Statist.,7, 1144–1147.
Takeuchi, K. and Akahira, M. (1975). Characterizations of prediction sufficiency (Adequacy) in terms of risk functions,Ann. Statist.,3, 1018–1024.
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Takada, Y. Invariant prediction rules and an adequate statistic. Ann Inst Stat Math 33, 91–100 (1981). https://doi.org/10.1007/BF02480922
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DOI: https://doi.org/10.1007/BF02480922