TRES 1.1.5

Major changes

Revise the help documentation for the function OptStiefelGBB.R.
The Journal of Statistical Software paper accompanying this package has been published.

We change the title from Tensor Regression with Envelope Structure and Three Generic Envelope Estimation Approaches'' toTensor Regression with Envelope Structure’’.

Revert res <- kroncov(En) to res <- try(kroncov(En)) in function TRR.fit, which is forgotten to be reverted in last version.

Replace the base::norm(x, 'F') function with sqrt(sum(x^2)) for some matrix x.
In the Data segment of the printout of the tensor object, instead of just the first few elements, the summarized results of all elements are printed.

Add more output information returned from OptManiMulitBallGBB() to the output of ballGBB1D().

Renaming: TRR_sim -> TRRsim; TPR_sim -> TPRsim; TensEnv_dim -> TRRdim; ballGBB1D_bic -> oneD_bic; TensPLS_cv2d3d -> TPRdim; OptimballGBB1D -> OptM1D; EnvMU -> simplsMU
Deprecate:
plot.Tenv:
- Correct the direction of y axis. The coordinates of x and y increase from left to right, top to bottom;
- Add arguments xlab = "", ylab = "", axes = TRUE, ask = TRUE, remove arguments xticks, yticks. axes is a logical value specifying whether the axes should be drawn. If ask = TRUE, user is prompted before the second plot is shown (if exists).
ECD, simplsMU, manifold1D, manifoldFG, OptM1D, OptMFG: Change optional arguments like maxiter, tol, to three dots ...
fun1D, get_ini1D, ballGBB1D, OptManiMulitBallGBB: Collected into file “1Dfunction.R”. Help documentation are no longer supported.
MenvU_sim: An option wishart = FALSE is provided to return the population matrices M and U. Other argument like jitter is also provided which adds an scaler matrix to M to ensures it positive-definiteness.
PMSE: Calculates the prediction and mean squared error for both TRR and TPR models.
kroncov: Add convergence criterion tol and the maximal iteration maxiter.

OptStiefelGBB: Hide out from the output.
manifoldFG: Set default value for Gamma_init.
ttt.R: Change arguments X,Y to x,y.
oneD_bic: Add the estimated envelope basis Gamma to the output.
TRRdim: Output the mean squared error using the selected envelope basis.
TRRdim, oneD_bic: Argument multiD is changed to C to comply with the paper Zhang X, Mai Q (2018). “Model-Free Envelope Dimension Selection.” Electronic Journal of Statistics.

OptMFG: New FG optimization function encapsulating the core function OptStiefelGBB.
show: overloads show in package rTensor. With the overloaded show, only the first 6 elements of tensor is printed out.

In documentation of subspace(), the formula of subspace distance should be ||P_{A} - P_{B}||_F/√{2d}.
Fix bat dataset where x was not binary.

Lists or environments data structures are also acceptable as a whole in TRR.fit() and TPR.fit(). They can be passed to argument x.
Since the variance-covariance matrix is not available for Tenv class object, we remove S3 methods vcov.Tenv(). Use function std_err() if the standard error for the tensor coefficient from TRR.fit() is desired.
Improved the computation efficiency by adopting cholesky decomposition in matrix inversion and the calculation of the square root of a matrix.
Add a real data set EEG. Refer to R help documentation for more details
Add a new feature to predict.Tenv(): if the argument newdata is missing, the fitted values from the fitted model is returned.

Change arguments Xn and Yn in all functions to x and y in accordance with other popular functions, e.g., lm(), glm(), etc.
plot.Tenv(): Change the name of argument thrd to level.
kroncov: Data Tn is centered before the estimation.

Add some references in Description field in file DESCRIPTION
Fix the document of summary.Tenv.
Remove the parameter ask in plot.Tenv.
Add envelope basis Gamma list into bat and square datasets.
Change the names of some parameters, like bic_max to maxdim in TensEnv_dim, max_iter to maxiter in manifold1D, epsilon to tol in ECD, G_ini to Gamma_init in manifoldFG, G_hat to Gamma in manifoldFG, Yhat to pred in PMSE.
Rename TRR, TPR as TRR.fit, TPR,fit.

print.Tenv: Prints the call, coefficients from TPR and TRR, make the output more concise.
print.summary.Tenv: Print call, dimensions of X, Y, sample size, mse, the coefficient and p_value. (invoked implicitly when there is no assignment of summary.Tenv).

Switch the arguments Xn and Yn in functions: TensEnv_dim, TensPLS_cv2d3d, Tenv, Tenv_Pval, TPR and TRR.
Removed package mvtnorm in DESCRIPTION, it is not used in the package.
Move all the packages in Depends in DESCRIPTION to Imports except for ManifoldOptim.
Add examples to some functions: PMSE, TensEnv_dim, TensPLS_cv2d3d, Tenv_Pval.
Add simulated data “bat” and “square” with which users can quickly verify the functions in the package.

# Usage
> data("bat")
> data("square")

TPR, TRR:
- Change the output names of some functions. E.g., Bhat in the object returned from TPR and TRR is renamed as coefficients.
- Append fitted.values and residuals into the output.
- More robust to the input type: Yn can be vector or matrix and Xn can be matrix, array or tensor for TPR, Xn can be vector or matrix and Yn can be matrix, array or tensor for TRR.
- Incorporate FG_TRR and FG_TPR into TRR and TPR. Add one more option for method, “FG”. Also add argument Gamma_init for “FG” method.
Tenv_Pval: Change the data type of outputs from array to tensor. Change the name se_mat to se.
PMSE: Rewrite PMSE. Xn can be matrix, array or tensor, Yn can be vector or matrix, and Bhat can be vector, matrix, array or tensor as long as the dimensions match the ones of Xn and Yn.
TRR_sim, TPR_sim: Add two simulation functions to generate data used in TRR and TPR which can help user quickly test the functions.

Construct S3 object for TRR and TPR with class attribute “Tenv”

> data("bat")
> fit <- TRR(bat$Xn, bat$Yn, method = "standard")
> class(fit)
> [1] "Tenv"

predict.Tenv: Make predictions of new data.
summary.Tenv: Append dimensions of X,Y, sample size, mse, p_val and s.e. to the output object from TPR and TRR.
plot.Tenv: Draw the plot of coefficients from TRR and TPR, and draw p_val plot from TRR.
vcov.Tenv: No covariance for coefficients. But for TRR, we print the standard error for coefficients.
fitted.default: Calculates the fitted Y for TPR and TRR separately.
residuals.default: Calculate Y minus fitted Y for TPR and TRR
coef.default: Print the coefficients for TPR and TRR.

FG_TPR, FG_TRR > Help pages for deprecated functions are available at help("TRES-deprecated").