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Title: Estimation of polynomials in the regression model (English)
Author: Volaufová, Júlia
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 27
Issue: 3
Year: 1982
Pages: 223-231
Summary lang: English
Summary lang: Slovak
Summary lang: Russian
Category: math
Summary: Let $\bold Y$ be an $n$-dimensional random vector which is $N_n(\bold {A0,K})$ distributed. A minimum variance unbiased estimator is given for $f(o)$ provided $f$ is an unbiasedly estimable functional of an unknown $k$-dimensional parameter $\bold 0$. (English)
Keyword: estimation of polynomials
Keyword: regression model
Keyword: general linear model
Keyword: BLUE
Keyword: unbiased estimate
Keyword: generalized Hermitian polynomial
MSC: 62F10
MSC: 62J05
idZBL: Zbl 0495.62069
idMR: MR0658004
DOI: 10.21136/AM.1982.103964
Date available: 2008-05-20T18:19:20Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] N. Aronszajn: Theory of Reproducing Kernels.Trans. Amer. Math. Soc. 68 (1950), 337 - 404. Zbl 0037.20701, MR 0051437, 10.1090/S0002-9947-1950-0051437-7
Reference: [2] G. Kallianpur: The Role of RKHS in the Study of Gaussian Processes.In Advances in Probability, vol. 2, M. Dekker INC., New York 1970, 59-83. MR 0283866
Reference: [3] I. A. Ibragimov J. A. Rozanov: Gaussovskie slučajnye procesy.Nauka, Moskva 1970. MR 0272040
Reference: [4] A. Pázman: Optimal Designs for the Estimation of Polynomial Functionals.Kybernetika 17 (1981) (in print.) MR 0629346
Reference: [5] R. C. Rao: Lineární metody statistické indukce a jejich aplikace.Academia, Praha 1978.
Reference: [6] R. C. Rao S. K. Mitra: Generalized Inverse of Matrices and Its Applications.John Willey, New York 1971. MR 0338013
Reference: [7] F. Štulajter: Nonlinear Estimators of Polynomials in Mean Values of a Gaussian Stochastic Process.Kybernetika 14 (1978), 3, 206-220. MR 0506650


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