# Tensor Regression with Envelope Structure

## Documentation for package ‘TRES’ version 1.1.5

- DESCRIPTION file.

## Help Pages

TRES-package | Tensor Regression with Envelope Structure
bat | Bat simulated data
ECD | ECD algorithm for estimating the envelope subspace
EEG | Electroencephalography (EEG) dataset for alcoholism study.
FGfun | The Objective function and its gradient
kroncov | The covariance estimation of tensor normal distribution
manifold1D | Estimate the envelope subspace ('ManifoldOptim' 1D)
manifoldFG | Estimate the envelope subspace ('ManifoldOptim' FG)
MenvU_sim | Generate matrices M and U
oneD_bic | Envelope dimension selection based on 1D-BIC
OptM1D | Estimate the envelope subspace ('OptM' 1D)
OptMFG | Estimate the envelope subspace ('OptM' FG)
OptStiefelGBB | Optimization on Stiefel manifold
plot.Tenv | Plot coefficients and p-value for Tenv object.
PMSE | Prediction and mean squared error.
predict.Tenv | Predict method for Tenv object.
print.summary.Tenv | Summarize method for Tenv object.
simplsMU | SIMPLS-type algorithm for estimating the envelope subspace
square | Square simulated data
std_err | Elementwise standard error.
subspace | The distance between two subspaces.
summary.Tenv | Summarize method for Tenv object.
Tenv_Pval | The p-value and standard error of coefficient in tensor response regression (TRR) model.
TPR | Tensor predictor regression
TPR.fit | Tensor predictor regression
TPRdim | Envelope dimension by cross-validation for tensor predictor regression (TPR).
TPRsim | Generate simulation data for tensor predictor regression (TPR)
TRES | Tensor Regression with Envelope Structure
TRR | Tensor response regression
TRR.fit | Tensor response regression
TRRdim | Envelope dimension selection for tensor response regression (TRR)
TRRsim | Generate simulation data for tensor response regression (TRR)
ttt | Matrix product of two tensors