Article
Keywords:
estimation of polynomials; regression model; general linear model; BLUE; unbiased estimate; generalized Hermitian polynomial
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 $\bold 0$.
References:
[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
[3] I. A. Ibragimov J. A. Rozanov:
Gaussovskie slučajnye procesy. Nauka, Moskva 1970.
MR 0272040
[4] A. Pázman:
Optimal Designs for the Estimation of Polynomial Functionals. Kybernetika 17 (1981) (in print.)
MR 0629346
[5] R. C. Rao: Lineární metody statistické indukce a jejich aplikace. Academia, Praha 1978.
[6] R. C. Rao S. K. Mitra:
Generalized Inverse of Matrices and Its Applications. John Willey, New York 1971.
MR 0338013
[7] F. Štulajter:
Nonlinear Estimators of Polynomials in Mean Values of a Gaussian Stochastic Process. Kybernetika 14 (1978), 3, 206-220.
MR 0506650