shapes (version 1.2.7)

estcov: Weighted Frechet mean of covariance matrices

Description

Computes the weighted Frechet means of an array of covariance matrices, with different options for the covariance metric. Also carries out principal co-ordinate analysis of the covariance matrices

Usage

estcov(S , method="Riemannian",weights=1,alpha=1/2,MDSk=2)

Value

A list with values

mean

The weighted mean covariance matrix

sd

The weighted standard deviation

pco

Principal co-ordinates (from multidimensional scaling with the metric)

eig

The eigenvalues from the principal co-ordinate analysis

Arguments

S

Input an array of covariance matrices of size k x k x n where each matrix is square, symmetric and positive definite

method

The type of distance to be used: "Procrustes": Procrustes size-and-shape metric, "ProcrustesShape": Procrustes metric with scaling, "Riemannian": Riemannian metric, "Cholesky": Cholesky based distance, "Power: Power Euclidean, with power alpha, "Euclidean": Euclidean metric, "LogEuclidean": Log-Euclidean metric, "RiemannianLe": Another Riemannian metric.

weights

The weights to be used for calculating the mean. If weights=1 then equal weights are used, otherwise the vector must be of length n.

alpha

The power to be used in the power Euclidean metric

MDSk

The number of MDS components in the principal co-ordinate analysis

Author

Ian Dryden

References

Dryden, I.L., Koloydenko, A. and Zhou, D. (2009). Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Annals of Applied Statistics, 3, 1102-1123.

See Also

distcov

Examples

S <- array(0,c(5,5,10) )
for (i in 1:10){
tem <- diag(5)+.1*matrix(rnorm(25),5,5)
S[,,i]<- tem
}

estcov( S , method="Procrustes")