minormalavar: minormalavar

In VecDep: Measuring Copula-Based Dependence Between Random Vectors

minormalavar

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 computes the asymptotic variance of the plug-in estimator for the correlation-based mutual information between \mathbf{X}_{1},...,\mathbf{X}_{k} given the entire correlation matrix \mathbf{R}.

Usage

minormalavar(R, dim)

Arguments

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

Details

The asymptotic variance of the plug-in estimator \mathcal{D}_{t \ln(t)}(\widehat{\mathbf{R}}_{n}) is computed at \mathbf{R}, where \widehat{\mathbf{R}}_{n} is the sample matrix of normal scores rank correlations. The underlying assumption is that the copula of \mathbf{X} is Gaussian.

Value

The asymptotic variance of the correlation-based mutual information between \mathbf{X}_{1},...,\mathbf{X}_{k}.

References

De Keyser, S. & Gijbels, I. (2024). Parametric dependence between random vectors via copula-based divergence measures. Journal of Multivariate Analysis 203:105336.
doi: https://doi.org/10.1016/j.jmva.2024.105336.

See Also

minormal for the computation of the mutual information, Helnormal for the computation of the Hellinger distance, Helnormalavar for the computation of the asymptotic variance of the plug-in estimator for the Hellinger distance, estR for the computation of the sample matrix of normal scores rank correlations.

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)))

minormalavar(R,dim)

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