# On the relationship between the matrix operators, vech and vecd

Research output: Contribution to journalArticle

### 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 1-17 17 Communications in Statistics - Theory and Methods https://doi.org/10.1080/03610926.2017.1353623 Accepted/In press - 2017 Aug 30

### Fingerprint

Operator Matrix
Operator
Heteroscedastic Model
Wald Test
Conditional Model
Multivariate Normal Distribution
Score Test
Relationships
Symmetric matrix
Coefficient

### Keywords

• Orthogonal matrix
• Permutation matrix
• Symmetric matrix
• vecd
• vech
• Wald test

### ASJC Scopus subject areas

• Statistics and Probability

### Cite this

In: Communications in Statistics - Theory and Methods, 30.08.2017, p. 1-17.

Research output: Contribution to journalArticle

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