Estimation of a quadratic function of the parameter of the mean in a linear model
Aplikace matematiky (1989)
- Volume: 34, Issue: 2, page 155-160
- ISSN: 0862-7940
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topVolaufová, Júlia, and Volauf, Peter. "Estimation of a quadratic function of the parameter of the mean in a linear model." Aplikace matematiky 34.2 (1989): 155-160. <http://eudml.org/doc/15572>.
@article{Volaufová1989,
abstract = {The paper deals with an optimal estimation of the quadratic function $\mathbf \{\beta ^\{\prime \}D\beta \}$, where $\beta \in \mathcal \{R\}^k, \mathbf \{D\}$ is a known $k \times k$ matrix, in the model $\mathbf \{Y, X\beta , \sigma ^2I\}$. The distribution of $\mathbf \{Y\}$ is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix $\mathbf \{X\}$.},
author = {Volaufová, Júlia, Volauf, Peter},
journal = {Aplikace matematiky},
keywords = {best unbiased quadratic estimator; quadratic function; best unbiased estimator; linear model; best unbiased quadratic estimator; quadratic function; best unbiased estimator},
language = {eng},
number = {2},
pages = {155-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimation of a quadratic function of the parameter of the mean in a linear model},
url = {http://eudml.org/doc/15572},
volume = {34},
year = {1989},
}
TY - JOUR
AU - Volaufová, Júlia
AU - Volauf, Peter
TI - Estimation of a quadratic function of the parameter of the mean in a linear model
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 2
SP - 155
EP - 160
AB - The paper deals with an optimal estimation of the quadratic function $\mathbf {\beta ^{\prime }D\beta }$, where $\beta \in \mathcal {R}^k, \mathbf {D}$ is a known $k \times k$ matrix, in the model $\mathbf {Y, X\beta , \sigma ^2I}$. The distribution of $\mathbf {Y}$ is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix $\mathbf {X}$.
LA - eng
KW - best unbiased quadratic estimator; quadratic function; best unbiased estimator; linear model; best unbiased quadratic estimator; quadratic function; best unbiased estimator
UR - http://eudml.org/doc/15572
ER -
References
top- J. Kleffe, Simultaneous Estimation of Expectation and Covariance Matrix in Linear Models, Math. Operationsforsch. Statist., Ser. Statistics, Vol. 9 (1978) No. 3, 443-478. (1978) Zbl0415.62026MR0522072
- J. Volaufová, Estimation of Polynomials in the Regression Model, Aplikace matematiky, Vol. 27 (1982), No. 3, 223-231. (1982) MR0658004
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