covres {Tlasso}

Sample Covariance Matrix of Residuals

Description

Generate sample covariance matrix of residuals (includes diagnoal) described in Lyu et al. (2019).

Usage

covres(data, Omega.list, k = 1)

Arguments

data

tensor object stored in a m1 * m2 * ... * mK * n array, where n is sample size and mk is dimension of the kth tensor mode.

Omega.list

list of precision matrices of tensor, i.e., Omega.list[[k]] is precision matrix for the kth tensor mode, k \in \{1 , \ldots, K\}.

k

index of interested mode, default is 1.

Details

This function computes sample covariance of residuals and is the basis for support recovery procedure in Lyu et al. (2019). Note that output matrix includes diagnoal while bias corrected matrix (output of biascor) for inference is off-diagnoal, see Lyu et al. (2019) for details. Elements in Omega.list are true precision matrices or estimation of the true ones, the latter can be output of Tlasso.fit.

Value

A matrix whose (i,j) entry (includes diagnoal) is sample covariance of the ith and jth residuals in the kth mode. See Lyu et al. (2019) for details.

Author(s)

Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu, Jian Yang, Guang Cheng.

See Also

varcor, biascor

Examples

m.vec = c(5,5,5)  # dimensionality of a tensor 
n = 5   # sample size 
k=1 # index of interested mode
lambda.thm = 20*c( sqrt(log(m.vec[1])/(n*prod(m.vec))), 
                   sqrt(log(m.vec[2])/(n*prod(m.vec))), 
                   sqrt(log(m.vec[3])/(n*prod(m.vec))))
DATA=Trnorm(n,m.vec,type='Chain') 
# obersavations from tensor normal distribution
out.tlasso = Tlasso.fit(DATA,T=1,lambda.vec = lambda.thm)   
# output is a list of estimation of precision matrices
rho=covres(DATA, out.tlasso, k = k) # sample covariance of residuals, including diagnoal 
rho