Abstract
A connection between invariance and sufficiency is established for the general case of the theory of linear statistical inference studied in the previous paper, and a counterpart of the simplest exponential family is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
E. Lehmann, Testing Statistical Hypotheses, Wiley, New York (1959).
O. V. Gerlein and A. M. Kagan, “Hilbert space methods in classical problems of mathematical statistics,” J. Sov. Mat.,12, No. 2 (1979).
T. S. Ferguson, Mathematical Statistics, Academic Press, New York (1967).
N. Dunford and J. T. Schwartz, Linear Operators, Vol. 3, Interscience, New York (1958).
E. Hille and R. Phillips, Functional Analysis and Semigroups, Am. Math. Soc. Colloquium Publications, Providence, Rhode Island (1957).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 53, pp. 101–106, 1975.
Rights and permissions
About this article
Cite this article
Gerlein, O.V. Invariant linear statistical inference. J Math Sci 12, 213–217 (1979). https://doi.org/10.1007/BF01262719
Issue Date:
DOI: https://doi.org/10.1007/BF01262719