The linear model with variance-covariance components and jackknife estimation

Kudeláš, Jaromír. "The linear model with variance-covariance components and jackknife estimation." Applications of Mathematics 39.2 (1994): 111-125. <http://eudml.org/doc/32874>.

@article{Kudeláš1994,
abstract = {Let $\theta ^*$ be a biased estimate of the parameter $\vartheta $ based on all observations $x_1$, $\dots $, $x_n$ and let $\theta _\{-i\}^*$ ($i=1,2,\dots ,n$) be the same estimate of the parameter $\vartheta $ obtained after deletion of the $i$-th observation. If the expectation of the estimators $\theta ^*$ and $\theta _\{-i\}^*$ are expressed as \[ \begin\{@align\}\{1\}\{-1\}\mathrm \{E\}(\theta ^*)&=\vartheta +a(n)b(\vartheta ) \\ \mathrm \{E\}(\theta \_\{-i\}^*)&=\vartheta +a(n-1)b(\vartheta )\qquad i=1,2,\dots ,n, \end\{@align\}\] where $a(n)$ is a known sequence of real numbers and $b(\vartheta )$ is a function of $\vartheta $, then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased estimator of the parameter $\vartheta $.},
author = {Kudeláš, Jaromír},
journal = {Applications of Mathematics},
keywords = {Jackknife estimator; least squares estimator; linear model; estimator of variance-covariance components; consistency; estimator of variance-covariance components; consistency; deletion of observations; Gauss-Markov estimator; biased estimate; linear model; least squares method; generalized jackknife estimator; unbiased estimator},
language = {eng},
number = {2},
pages = {111-125},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The linear model with variance-covariance components and jackknife estimation},
url = {http://eudml.org/doc/32874},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Kudeláš, Jaromír
TI - The linear model with variance-covariance components and jackknife estimation
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 2
SP - 111
EP - 125
AB - Let $\theta ^*$ be a biased estimate of the parameter $\vartheta $ based on all observations $x_1$, $\dots $, $x_n$ and let $\theta _{-i}^*$ ($i=1,2,\dots ,n$) be the same estimate of the parameter $\vartheta $ obtained after deletion of the $i$-th observation. If the expectation of the estimators $\theta ^*$ and $\theta _{-i}^*$ are expressed as \[ \begin{@align}{1}{-1}\mathrm {E}(\theta ^*)&=\vartheta +a(n)b(\vartheta ) \\ \mathrm {E}(\theta _{-i}^*)&=\vartheta +a(n-1)b(\vartheta )\qquad i=1,2,\dots ,n, \end{@align}\] where $a(n)$ is a known sequence of real numbers and $b(\vartheta )$ is a function of $\vartheta $, then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased estimator of the parameter $\vartheta $.
LA - eng
KW - Jackknife estimator; least squares estimator; linear model; estimator of variance-covariance components; consistency; estimator of variance-covariance components; consistency; deletion of observations; Gauss-Markov estimator; biased estimate; linear model; least squares method; generalized jackknife estimator; unbiased estimator
UR - http://eudml.org/doc/32874
ER -