Abstract
The problem of the statistical estimation of quadratic polynomials of the parameters of the normal law is considered.
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References
Yu. V. Linnik, Statistical Problems with Nuisance Parameters [in Russian], Nauka, Moscow (1966).
P. Cheng, Q. G. Wu, and G. Y. Li, Admissibility of quadratic estimates of 2-order moment about the origin," Acta Math. Appl. Sinica,6, No. 1, 18–28 (1983).
R. H. Farrell, "On a necessary and sufficient condition for admissibility of estimators when strictly convex loss is used," Ann. Math. Statist.,39, No. 1, 23–28 (1968).
A. L. Rukhin, "Quadratic estimators of quadratic functions of normal parameters," J. Statist. Plann. Inference,15, No. 3, 301–310 (1987).
C. Stein, "Approximation of improper prior measures by prior probability measures," in: Bernoulli, Bayes, Laplace Anniversary Volume, Springer, New York (1965), pp. 217–240.
Q. G. Wu, P. Cheng, and G. Y. Li, "Admissibility of quadratic estimates of error variance in linear models," Sci. Sinica Ser. A,25, No. 2, 113–124 (1982).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 234–247, 1990.
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Rukhin, A.L. Admissible polynomial estimators for quadratic polynomials of normal parameters. J Math Sci 68, 566–576 (1994). https://doi.org/10.1007/BF01254283
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DOI: https://doi.org/10.1007/BF01254283