covCSE {covKCD}

Empirical Bayes core shrinkage covariance estimator

Description

Estimate a covariance matrix by adaptively shrinking the core.

Usage

covCSE(data, n = NULL, p1 = NULL, p2 = NULL, tol = 1e-08)

Arguments

data

either a numeric n*p1*p2 array consisting of n data matrices each of dimension p1*p2, or a p1*p2 covariance matrix of data of this type. If the latter, the values of n, p1 and p2 must be specified.

n

the sample size.

p1

the row dimension of the data matrices.

p2

the column dimension of the data matrices.

tol

the convergence tolerance of the iterative algorithm.

Value

a covariance matrix of the same dimension as S. The attribute w of S gives the shrinkage weight on the Kronecker covariance of S.

Author(s)

Peter Hoff

Examples

p1<-4 ; p2<-3 ; n<-20

# create a matrix Y with separable covariance
Sig1<-rWishart(1,p1,diag(p1))[,,1] 
Sig2<-rWishart(1,p2,diag(p2))[,,1] 

Y<-array(rnorm(n*p1*p2),dim=c(n,p1,p2))  
Y<-aperm( apply(Y,c(1,3),function(y){ msqrt(Sig1)%*%y } ),c(2,1,3)) 
Y<-aperm( apply(Y,c(1,2),function(y){ msqrt(Sig2)%*%y } ),c(2,3,1)) 

# covariance 
S<-mcov(Y) 
covCSE(S,n,p1,p2)  

# now an unstructured covariance
S<-rWishart(1,p1*p2,diag(p1*p2))[,,1] 
covCSE(S,n,p1,p2)