# varcor: Variance Correction of Sample Covariance of Residuals In Tlasso: Non-Convex Optimization and Statistical Inference for Sparse Tensor Graphical Models

## Description

Generate variance correction term of sample covariance of residuals described in Sun et al. (2016).

## Usage

 `1` ```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, 1 <= k <= 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 Sun et al. (2016).

## Value

A scalar of variance correction for the kth mode.

## Author(s)

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

`varcor`, `biascor`, `covres`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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 ```