In this note we demonstrate the inadmissibility of an extensive class of polynomial estimates of the shift parameter in the case of a quadratic loss function.
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A. M. Kagan, Yu. V. Linnik, and C. R. Rao, “On a characterization of the normal law based on a property of the sample average,” Sankhya, Ser. A,27, No. 3–4, 405–406 (1965).
A. M. Kagan, “Theory of estimation for families with shift, scaling, and exponentiation parameters,” Trudy Matem. Inst. Akad. Nauk SSSR.104 (1968).
A. M. Kagan, Yu. V. Linnik, and C. R. Rao, Characterizational Problems of Mathematical Statistics [in Russian], Moscow (1972).
A. A. Zinger, “Independence of quasipolynomial statistics and analytical properties of distributions,” Teor. Veroyatn. i ee Primen.,3, No. 3, 262–284 (1958).
V. V. Golubev, Lectures on the Analytic Theory of Differential Equations [in Russian], Moscow-Leningrad (1950).
Yu. V. Linnik, “On polynomial statistics in connection with the analytic theory of differential equations,” Vestnik Leningrad Gos. Univ.,1, 35–48 (1956).
J. Marcinkiewicz, “Sur une propriete de la loi de Gauss,” Math. Zeitschr.,44, No. 4–5, 622–638 (1938).
H. Wittich, Recent Research on Single-Valued Analytic Functions [Russian translation], Moscow (1960).
Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 885–894, December, 1973.
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Klebanov, L.B. Inadmissibility of polynomial estimates of the shift parameter. Mathematical Notes of the Academy of Sciences of the USSR 14, 1068–1073 (1973). https://doi.org/10.1007/BF01099594
- Loss Function
- Polynomial Estimate
- Shift Parameter
- Quadratic Loss
- Extensive Class