signal {Tlasso}

Regression Parameter of Conditional Linear Model

Description

Compute regression parameter of conditional linear model of separable tensor normal distribution described in Lyu et al. (2019).

Usage

signal(Omega.list, i = 1, k = 1)

Arguments

Omega.list

list of precision matrices of tensor, i.e., Omega.list[[k]] is the kth precision matrix. Omega.list can be either true precision matrices or output of Tlasso.fit. for the kth tensor mode, k \in \{1 , \ldots, K\}.

i

index of interested regression parameter, default is 1. See details in Lyu et al. (2019).

k

index of interested mode, default is 1.

Details

This function computes regression parameter and is fundamental for sample covariance of residuals and bias correction. See details in Lyu et al. (2019).

Value

A vector of regression paramter.

Author(s)

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

See Also

covres, 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
signal(out.tlasso, i=2 , k=k )
# the regression parameter for conditional linear model of 2rd row in 1st mode