varcor {Tlasso}

Variance Correction of Sample Covariance of Residuals

Description

Generate variance correction term of sample covariance of residuals described in Lyu et al. (2019).

Usage

varcor(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\}. Elements in Omega.list are true precision matrices or estimation of the true ones, the latter can be output of Tlasso.fit.

k

index of interested mode, default is 1.

Details

This function computes variance correction term of sample covariance of residuals and is utilized to normalize test statistic into standord normal, see Lyu et al. (2019).

Value

A scalar of variance correction for the kth mode.

Author(s)

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

See Also

varcor, biascor, covres

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 
varpi2=varcor(DATA, out.tlasso, k = k)
# variance correction term for kth mode's sample covariance of residuals