Abstract
We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | Communications in Statistics - Theory and Methods |
| DOIs | |
| Publication status | Accepted/In press - 2017 Aug 30 |
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Keywords
- Orthogonal matrix
- Permutation matrix
- Symmetric matrix
- vecd
- vech
- Wald test
ASJC Scopus subject areas
- Statistics and Probability
Cite this
On the relationship between the matrix operators, vech and vecd. / Nagakura, Daisuke.
In: Communications in Statistics - Theory and Methods, 30.08.2017, p. 1-17.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the relationship between the matrix operators, vech and vecd
AU - Nagakura, Daisuke
PY - 2017/8/30
Y1 - 2017/8/30
N2 - We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively.
AB - We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively.
KW - Orthogonal matrix
KW - Permutation matrix
KW - Symmetric matrix
KW - vecd
KW - vech
KW - Wald test
UR - http://www.scopus.com/inward/record.url?scp=85028742742&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028742742&partnerID=8YFLogxK
U2 - 10.1080/03610926.2017.1353623
DO - 10.1080/03610926.2017.1353623
M3 - Article
AN - SCOPUS:85028742742
SP - 1
EP - 17
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
ER -