Description Usage Arguments Details Value Author(s) See Also Examples
Generate a matrix of bias-corrected sample covariance of residuals (excludes diagnoal) described in Lyu et al. (2019).
1 | biascor(rho, Omega.list, k = 1)
|
rho |
matrix of sample covariance of residuals (includes diagnoal), e.g., output of |
Omega.list |
list of precision matrices of tensor, i.e., |
k |
index of interested mode, default is 1. |
This function computes bias-corrected sample covariance of residuals (excludes diagnoal, diagnoal is zero vector).
Note that output matrix excludes diagnoal while sample covariance of residuals includes 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
.
A matrix whose (i,j) entry (excludes diagnoal; diagnoal is zero vector) is bias-corrected sample covariance of the ith and jth residuals in the kth mode. See Lyu et al. (2019) for details.
Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu, Jian Yang, Guang Cheng.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | 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
bias_rho=biascor(rho,out.tlasso,k=k)
bias_rho # bias-corrected sample covariance of residuals
# diagnoal is zero vector
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