Description Introduction Tensr functions References

This package provides a collection of functions for likelihood and equivariant inference for covariance matrices under the array normal model. Also included are functions for calculating tensor decompositions that are related to likelihood inference in the array normal model.

Let *X* be a multidimensional array
(also called a tensor) of K dimensions. This package provides a
series of functions to perform statistical inference when

*vec(X) \sim N(0,Σ),*

where *Σ* is assumed to
be Kronecker structured. That is, *Σ* is the Kronecker
product of *K* covariance matrices, each of which has the
interpretation of being the covariance of *X* along its
*k*th mode, or dimension.

Pay particular attention to the zero mean assumption. That is,
you need to de-mean your data prior to applying these
functions. If you have more than one sample, *X_i* for *i
= 1,…,n*, then you can concatenate these tensors along a
*(K+1)*th mode to form a new tensor *Y* and apply the
`demean_tensor()`

function to Y which will return a tensor
that satisfies the mean-zero assumption.

The details of the methods in this package can be found in Gerard and Hoff (2015) and Gerard and Hoff (2016).

`amprod`

*k*-mode product.

`anorm_cd`

Array normal conditional distributions.

`array_bic_aic`

Calculate the AIC and BIC.

`arrIndices`

Array indices.

`atrans`

Tucker product.

`collapse_mode`

Collapse multiple modes into one mode.

`convert_cov`

Convert the output from `equi_mcmc`

to
component covariance matrices.

`demean_tensor`

Demeans array data.

`equi_mcmc`

Gibbs sampler using an invariant prior.

`fnorm`

Frobenius norm of an array.

`get_equi_bayes`

Get the Bayes rule under multiway Stein's
loss.

`get_isvd`

Calculate the incredible SVD (ISVD).

`holq`

Calculate the incredible higher-order LQ decomposition
(HOLQ).

`hooi`

Calculate the higher-order orthogonal iteration (HOOI).

`hosvd`

Calculate the (truncated) higher-order SVD (HOSVD).

`Kom`

Commutation matrix.

`ihop`

The incredible higher-order polar decomposition (IHOP).

`ldan`

Log-likelihood of array normal model.

`listprod`

Element-wise matrix products between two lists.

`lq`

LQ decomposition.

`lrt_null_dist_dim_same`

Draw from null distribution of
likelihood ratio test statistic.

`lrt_stat`

Calculate the likelihood ratio test statistic.

`mat`

Unfold a matrix.

`mhalf`

The symmetric square root of a positive definite
matrix.

`mle_from_holq`

Get MLE from output of `holq`

.

`multi_stein_loss`

Calculate multiway Stein's loss from square
root matrices.

`multi_stein_loss_cov`

Calculate multiway Stein's loss from
component covariance matrices.

`multiway_takemura`

Calculate a truncated multiway Takemura
estimator.

`polar`

The left polar decomposition.

`qr2`

QR Decomposition.

`random_ortho`

Generate a list of orthogonal matrices drawn
from Haar distribution.

`rmirror_wishart`

Sample from the mirror-Wishart distribution.

`sample_sig`

Update for total variation parameter in
`equi_mcmc`

.

`sample_right_wishart`

Gibbs update of `Phi_inv`

.

`start_ident`

Get list of identity matrices.

`start_resids`

Sample covariance matrices for each mode.

`tsum`

Tucker sum.

`tr`

Trace of a matrix.

`trim`

Truncates small numbers to 0.

Gerard, D., & Hoff, P. (2016). A higher-order LQ
decomposition for separable covariance models.
*Linear Algebra and its Applications*, 505, 57-84.
https://doi.org/10.1016/j.laa.2016.04.033
http://arxiv.org/pdf/1410.1094v1.pdf

Gerard, D., & Hoff, P. (2015). Equivariant minimax
dominators of the MLE in the array normal model.
*Journal of Multivariate Analysis*, 137, 32-49.
https://doi.org/10.1016/j.jmva.2015.01.020
http://arxiv.org/pdf/1408.0424.pdf

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.