kroncov: The covariance estimation of a tensor random variable

In kusakehan/TEReg: An R package for tensor envelope regression with tensor response and tensor predictor

Description

This function estimates the covariance of a tensor random variable. We assume the covariance of the tensor r.v. has a seperable Kronecker covariance structure, i.e. \boldsymbol{Σ}=\boldsymbol{Σ}_{m}\otimes\cdots\otimes\boldsymbol{Σ}_{1}. This algorithm is described in Manceur, A. M., & Dutilleul, P. (2013).

Usage

kroncov(Tn)

Arguments

Tn	A p_1\times\cdots p_m\times n data array, where n is the sample size.

Value

lambda	The normalizing constant.
S	A matrix lists with each element being the individual estimation of the seperable Kronecker covariance element \boldsymbol{Σ}_m,…,\boldsymbol{Σ}_1.

References

Manceur, A. M., & Dutilleul, P. (2013). Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion. Journal of Computational and Applied Mathematics, 239, 37-49.

kusakehan/TEReg documentation built on May 30, 2019, 7:17 a.m.