On the relationship between the matrix operators, vech and vecd

Daisuke Nagakura

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 13, 3252-3268

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1353623

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