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This package contains a collection of functions for statistical analysis with tensor(array)-variate data sets.
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 \(\text{vec}(X) \sim N(0,\Sigma)\), where \(\Sigma\) is assumed to be Kronecker structured. That is, \(\Sigma\) 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 \(i = 1,\ldots,n\), 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.
Details of the methods may be found in Gerard & Hoff (2015) and
Gerard & Hoff (2016). In particular, tensr
has the
following features:
This package is also published on CRAN.
Vignettes are available on Equivariant Inference and Likelihood Inference.
To install from CRAN, run in R
:
install.packages("tensr")
To install the latest version from Github, run in R
:
## install.packages("pak")
::pak("github::dcgerard/tensr") pak
Gerard, D., & Hoff, P. (2016). A higher-order LQ decomposition for separable covariance models. Linear Algebra and its Applications, 505, 57-84. doi: 10.1016/j.laa.2016.04.033
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49. doi: 10.1016/j.jmva.2015.01.020
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.