contr: Contraction matrix

In therimalaya/envelope: Computing Envelope Estimators in Multivariate Linear Regression

Description

Generate contraction matrix.

Usage

contr(d)

Arguments

d	Dimension of the contraction matrix. A positive integer.

Details

The contraction and expansion matrices are links between the "vec" operator and "vech"operator: for an d by d symmetric matrix A, vech(A) = contr(d) * vec(A), and vec(A) = expan(d) * vech(A). The "vec" operator stacks the matrix A into an d ^ 2 dimensional vector columnwise. The "vech" operator stacks the lower triangle or the upper triangle of a symmetric matrix into an d * (d + 1) / 2 vector. For more details of "vec", "vech", contraction and expansion matrix, refer to Henderson and Searle (1979).

Value

The output is a matrix.

contrMatrix

A contraction matrix that has dimension d * (d + 1) / 2 by d ^ 2.

References

Henderson, H. V., and Searle, S. R. (1979). Vec and Vech operators for matrices, with some uses in Jacobians and multivariate statistics. Canadian J. Statist. 7, 65 - 81.

Examples

contr(3)

therimalaya/envelope documentation built on May 29, 2019, 1:38 p.m.