The collection of correlation matrices is considered as a subset (and quotient) of the well-known SPD manifold. In our package, it is defined as $$\mathcal{C}_{++}^p = \lbrace X \in \mathbf{R}^{p\times p} ~\vert~ X^\top = X,~ \textrm{rank}(X)=p,~ \textrm{diag}(X) = 1 \rbrace$$ where the rank condition means it is strictly positive definite. Please note that the geometry involving semi-definite correlation matrices is not the objective here.
Arguments
- input
correlation data matrices to be wrapped as
riemdataclass. Following inputs are considered,- array
an \((p\times p\times n)\) array where each slice along 3rd dimension is a correlation matrix.
- list
a length-\(n\) list whose elements are \((p\times p)\) correlation matrices.
Value
a named riemdata S3 object containing
- data
a list of \((p\times p)\) correlation matrices.
- size
size of each correlation matrix.
- name
name of the manifold of interests, "correlation"
Examples
#-------------------------------------------------------------------
# Checker for Two Types of Inputs
#
# 5 observations; empirical correlation of normal observations.
#-------------------------------------------------------------------
# Data Generation
d1 = array(0,c(3,3,5))
d2 = list()
for (i in 1:5){
dat = matrix(rnorm(10*3),ncol=3)
d1[,,i] = stats::cor(dat)
d2[[i]] = d1[,,i]
}
# Run
test1 = wrap.correlation(d1)
test2 = wrap.correlation(d2)