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 languageEnglish
Pages (from-to)1-17
Number of pages17
JournalCommunications in Statistics - Theory and Methods
DOIs
Publication statusAccepted/In press - 2017 Aug 30

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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

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