Volaufová, Júlia, and Kubáček, Lubomír. "Locally and uniformly best estimators in replicated regression model." Aplikace matematiky 28.5 (1983): 386-390. <http://eudml.org/doc/15317>.
@article{Volaufová1983,
abstract = {The aim of the paper is to estimate a function $\gamma =tr(D\beta \beta ^\{\prime \})+tr(C\sum )$ (with $d, C$ known matrices) in a regression model $(Y, X\beta ,\sum )$ with an unknown parameter $\beta $ and covariance matrix $\sum $. Stochastically independent replications $Y_1,\ldots , Y_m$ of the stochastic vector $Y$ are considered, where the estimators of $X\beta $ and $\sum $ are $\bar\{Y\}=\frac\{1\}\{m\} \sum ^m _\{i=1\} Y_i$ and $\hat\{\sum \}=(m-1)^\{-1\} \sum ^m_\{i=1\}(Y_i-\bar\{Y\})(Y_i-\bar\{Y\})^\{\prime \}$, respectively. Locally and uniformly best inbiased estimators of the function $\gamma $, based on $\bar\{Y\}$ and $\hat\{\sum \}$, are given.},
author = {Volaufová, Júlia, Kubáček, Lubomír},
journal = {Aplikace matematiky},
keywords = {replicated regression model; best unbiased estimators; replicated regression model; best unbiased estimators},
language = {eng},
number = {5},
pages = {386-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Locally and uniformly best estimators in replicated regression model},
url = {http://eudml.org/doc/15317},
volume = {28},
year = {1983},
}
TY - JOUR
AU - Volaufová, Júlia
AU - Kubáček, Lubomír
TI - Locally and uniformly best estimators in replicated regression model
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 5
SP - 386
EP - 390
AB - The aim of the paper is to estimate a function $\gamma =tr(D\beta \beta ^{\prime })+tr(C\sum )$ (with $d, C$ known matrices) in a regression model $(Y, X\beta ,\sum )$ with an unknown parameter $\beta $ and covariance matrix $\sum $. Stochastically independent replications $Y_1,\ldots , Y_m$ of the stochastic vector $Y$ are considered, where the estimators of $X\beta $ and $\sum $ are $\bar{Y}=\frac{1}{m} \sum ^m _{i=1} Y_i$ and $\hat{\sum }=(m-1)^{-1} \sum ^m_{i=1}(Y_i-\bar{Y})(Y_i-\bar{Y})^{\prime }$, respectively. Locally and uniformly best inbiased estimators of the function $\gamma $, based on $\bar{Y}$ and $\hat{\sum }$, are given.
LA - eng
KW - replicated regression model; best unbiased estimators; replicated regression model; best unbiased estimators
UR - http://eudml.org/doc/15317
ER -