Estimation of polynomials in the regression model

Júlia Volaufová

Aplikace matematiky (1982)

  • Volume: 27, Issue: 3, page 223-231
  • ISSN: 0862-7940

Abstract

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Let 𝐘 be an n -dimensional random vector which is N n ( 𝐀 0 , 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 0 .

How to cite

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Volaufová, Júlia. "Estimation of polynomials in the regression model." Aplikace matematiky 27.3 (1982): 223-231. <http://eudml.org/doc/15241>.

@article{Volaufová1982,
abstract = {Let $\mathbf \{Y\}$ be an $n$-dimensional random vector which is $N_n(\mathbf \{A0,K\})$ distributed. A minimum variance unbiased estimator is given for $f(o)$ provided $f$ is an unbiasedly estimable functional of an unknown $k$-dimensional parameter $\mathbf \{0\}$.},
author = {Volaufová, Júlia},
journal = {Aplikace matematiky},
keywords = {estimation of polynomials; regression model; general linear model; BLUE; unbiased estimate; generalized Hermitian polynomial; estimation of polynomials; regression model; general linear model; BLUE; unbiased estimate; generalized Hermitian polynomial},
language = {eng},
number = {3},
pages = {223-231},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimation of polynomials in the regression model},
url = {http://eudml.org/doc/15241},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Volaufová, Júlia
TI - Estimation of polynomials in the regression model
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 3
SP - 223
EP - 231
AB - Let $\mathbf {Y}$ be an $n$-dimensional random vector which is $N_n(\mathbf {A0,K})$ distributed. A minimum variance unbiased estimator is given for $f(o)$ provided $f$ is an unbiasedly estimable functional of an unknown $k$-dimensional parameter $\mathbf {0}$.
LA - eng
KW - estimation of polynomials; regression model; general linear model; BLUE; unbiased estimate; generalized Hermitian polynomial; estimation of polynomials; regression model; general linear model; BLUE; unbiased estimate; generalized Hermitian polynomial
UR - http://eudml.org/doc/15241
ER -

References

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  1. N. Aronszajn, 10.1090/S0002-9947-1950-0051437-7, Trans. Amer. Math. Soc. 68 (1950), 337 - 404. (1950) Zbl0037.20701MR0051437DOI10.1090/S0002-9947-1950-0051437-7
  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. (1970) Zbl0234.60058MR0283866
  3. I. A. Ibragimov J. A. Rozanov, Gaussovskie slučajnye procesy, Nauka, Moskva 1970. (1970) MR0272040
  4. A. Pázman, Optimal Designs for the Estimation of Polynomial Functionals, Kybernetika 17 (1981) (in print.) (1981) Zbl0466.62067MR0629346
  5. R. C. Rao, Lineární metody statistické indukce a jejich aplikace, Academia, Praha 1978. (1978) 
  6. R. C. Rao S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Willey, New York 1971. (1971) Zbl0236.15004MR0338013
  7. F. Štulajter, Nonlinear Estimators of Polynomials in Mean Values of a Gaussian Stochastic Process, Kybernetika 14 (1978), 3, 206-220. (1978) Zbl0386.62072MR0506650

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