Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Oktaba, Wiktor. "Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model." Applications of Mathematics 40.1 (1995): 55-59. <http://eudml.org/doc/32903>.

@article{Oktaba1995,
abstract = {By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $|\sigma ^2\sum |$ in the MGM model $(U,XB, \sigma ^2\sum \otimes V)$, $ \sum >0$, scalar $\sigma ^2 > 0$, with a matrix $V \ge 0$. A known $n\times p$ random matrix $U$ has the expected value $E(U) = XB$, where the $n\times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d\times p$ matrix of parameters and $\sigma ^2\sum \otimes V$ is the covariance matrix of $U,\, \otimes $ being the symbol of the Kronecker product of matrices. A particular case of Srivastava and Khatri’s [4] theorem 2.2 was published by Anderson [1], p. 173, Th. 7.5.4, when $V=I$, $ \sigma ^2 = 1$, $ X=\text\{1\}$ and $B = \mu ^\{\prime \} = [\mu _1, \dots , \mu _p]$ is a row vector.},
author = {Oktaba, Wiktor},
journal = {Applications of Mathematics},
keywords = {generalized multivariate Gauss-Markoff model; singular covariance matrix; determinant; asymptotically normal confidence interval; product of independent chi-squares; multivariate central limit theorem; Wishart distribution; matrix of product sums for error; hypothesis and “total”; singular covariance matrix; product of independent chi-squares; multivariate central limit theorem; Wishart distribution; matrix of product sums for error; asymptotically normal confidence intervals; determinant; multivariate Gauss-Markov model; random matrix; experimental design; covariance matrix; Kronecker product},
language = {eng},
number = {1},
pages = {55-59},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model},
url = {http://eudml.org/doc/32903},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Oktaba, Wiktor
TI - Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 1
SP - 55
EP - 59
AB - By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $|\sigma ^2\sum |$ in the MGM model $(U,XB, \sigma ^2\sum \otimes V)$, $ \sum >0$, scalar $\sigma ^2 > 0$, with a matrix $V \ge 0$. A known $n\times p$ random matrix $U$ has the expected value $E(U) = XB$, where the $n\times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d\times p$ matrix of parameters and $\sigma ^2\sum \otimes V$ is the covariance matrix of $U,\, \otimes $ being the symbol of the Kronecker product of matrices. A particular case of Srivastava and Khatri’s [4] theorem 2.2 was published by Anderson [1], p. 173, Th. 7.5.4, when $V=I$, $ \sigma ^2 = 1$, $ X=\text{1}$ and $B = \mu ^{\prime } = [\mu _1, \dots , \mu _p]$ is a row vector.
LA - eng
KW - generalized multivariate Gauss-Markoff model; singular covariance matrix; determinant; asymptotically normal confidence interval; product of independent chi-squares; multivariate central limit theorem; Wishart distribution; matrix of product sums for error; hypothesis and “total”; singular covariance matrix; product of independent chi-squares; multivariate central limit theorem; Wishart distribution; matrix of product sums for error; asymptotically normal confidence intervals; determinant; multivariate Gauss-Markov model; random matrix; experimental design; covariance matrix; Kronecker product
UR - http://eudml.org/doc/32903
ER -