Summary method for object returned from TRR.fit and TPR.fit functions.
# S3 method for Tenv
summary(object, ...)# S3 method for summary.Tenv
print(x, ...)
Arguments to be passed to or from other methods.
An object of class "summary.Tenv", usually, a result of a call to summary.Tenv.
Return object with additional components
The method call
Sample size
Dimensions of predictor
Dimensions of response
The tensor coefficients estimated from TPR.fit or TRR.fit
The residuals, which equals to the response minus the fitted values
A list of envelope subspace basis
Mean squared error. The mean squared Frobenius norm of the difference between each response \(\mathbf{Y}_i\) and fitted value \(\hat{\mathbf{Y}}_i\), $$1/n\sum_{i=1}^n\|\mathbf{Y}_i-\hat{\mathbf{Y}}_i\|_F^2$$
Only for object returned from TRR.fit, p-value for coefficients
Only for object returned from TRR.fit, standard error for coefficients
Extract call, coefficients, residuals, Gamma from object.
The mean squared error mse is defined as \(1/n\sum_{i=1}^n\|\mathbf{Y}_i-\hat{\mathbf{Y}}_i\|_F^2\), where \(\hat{\mathbf{Y}}_i\) is the prediction and \(\|\cdot\|_F\) is the Frobenius norm of tensor.
For the object returned from TRR.fit, return the \(p\)-value and the standard error of estimated coefficient. However, since \(p\)-value and standard error depend on \(\widehat{\mathrm{cov}}^{-1}\{\mathrm{vec}(\mathbf{X})\}\) which is unavailable for the ultra-high dimensional \(\mathrm{vec}(\mathbf{X})\) in tensor predictor regression (TPR), the two statistics are not provided for the object returned from TPR.fit.
print.summary.Tenv gives a more readable format of the statistics contained in summary.Tenv. If object is from TRR.fit, then p-val and se are also returned.
Tenv_Pval is used to calculate the \(p\)-value and standard error.
PMSE is used to calculate mean squared error for any provided datasets and coefficient.
# NOT RUN {
data("bat")
x <- bat$x
y <- bat$y
fit <- TRR.fit(x, y, method="standard")
##print summary
summary(fit)
# }
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