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On the relationship between the matrix operators, vech and vecd

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  • Daisuke Nagakura

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.

Suggested Citation

  • Daisuke Nagakura, 2018. "On the relationship between the matrix operators, vech and vecd," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3252-3268, July.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:13:p:3252-3268
    DOI: 10.1080/03610926.2017.1353623
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