createR0: createR0

In VecDep: Measuring Copula-Based Dependence Between Random Vectors

createR0

Description

Given a q-dimensional random vector \mathbf{X} = (\mathbf{X}_{1},...,\mathbf{X}_{k}) with \mathbf{X}_{i} a d_{i}-dimensional random vector, i.e., q = d_{1} + ... + d_{k}, this function constructs the correlation matrix under independence of \mathbf{X}_{1},...,\mathbf{X}_{k}, given the entire correlation matrix \mathbf{R}.

Usage

createR0(R, dim)

Arguments

R	The correlation matrix of \mathbf{X}.
dim	The vector of dimensions (d_{1},...,d_{k}).

Details

Given a correlation matrix

\mathbf{R} = \begin{pmatrix} \mathbf{R}_{11} & \mathbf{R}_{12} & \cdots & \mathbf{R}_{1k} \\ \mathbf{R}_{12}^{\text{T}} & \mathbf{R}_{22} & \cdots & \mathbf{R}_{2k} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{R}_{1k}^{\text{T}} & \mathbf{R}_{2k}^{\text{T}} & \cdots & \mathbf{R}_{kk} \end{pmatrix},

the matrix \mathbf{R}_{0} = \text{diag}(\mathbf{R}_{11}, \dots, \mathbf{R}_{kk}), being the correlation matrix under independence of \mathbf{X}_{1}, \dots, \mathbf{X}_{k}, is returned.

Value

The correlation matrix under independence of \mathbf{X}_{1}, \dots, \mathbf{X}_{n}.

Examples

q = 10
dim = c(1,2,3,4)

# AR(1) correlation matrix with correlation 0.5
R = 0.5^(abs(matrix(1:q-1,nrow = q, ncol = q, byrow = TRUE) - (1:q-1)))

createR0(R,dim)

VecDep documentation built on April 4, 2025, 5:14 a.m.