estcov function

Weighted Frechet mean of covariance matrices

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

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

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

Returns

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

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.

Author(s)

Ian Dryden

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")