summary.Tenv {TRES}

Summarize method for Tenv object.

Description

Summary method for object returned from TRR.fit and TPR.fit functions.

Usage

## S3 method for class 'Tenv'
summary(object, ...)

## S3 method for class 'summary.Tenv'
print(x, ...)

Arguments

object

An object of class "Tenv", as the ones returned from TPR.fit or TRR.fit.

...

Additional arguments. No available arguments exist in this version.

x

An object of class "summary.Tenv", usually, a result of a call to summary.Tenv.

Details

Extract call, method, coefficients, residuals, Gamma from object. And append mse, p-value and the standard error of estimated coefficient.

The mean squared error mse is defined as 1/n\sum_{i=1}^n||Y_i-\hat{Y}_i||_F^2, where \hat{Y}_i is the prediction and ||\cdot||_F is the Frobenius norm of tensor.

Since the p-value and standard error depend on the estimation of cov^{-1}(vec(X)) which is unavailable for the ultra-high dimensional vec(X) in tensor predictor regression (TPR), the two statistics are only provided for the object returned from TRR.fit.

print.summary.Tenv provides a more readable form of the statistics contained in summary.Tenv. If object is returned from TRR.fit, then p-val and se are also returned.

Value

Return object with additional components

call

The matched call.

method

The implemented method.

n

The sample size.

xdim

The dimension of predictor.

ydim

The dimension of response.

coefficients

The tensor coefficients estimated from TPR.fit or TRR.fit.

residuals

The residuals, which equals to the response minus the fitted values.

Gamma

A list of envelope subspace basis.

mse

The mean squared error. The mean squared Frobenius norm of the difference between each response Y_i and fitted value \hat{Y}_i.

p_val

The p-value for coefficients. Only for the object returned from TRR.fit.

se

The standard error for coefficients. Only for the object returned from TRR.fit.

See Also

Fitting functions TRR.fit, TPR.fit.

Examples

data("bat")
x <- bat$x
y <- bat$y
fit <- TRR.fit(x, y, method="standard")
##print summary
summary(fit)

##Extract the p-value and standard error from summary
summary(fit)$p_val
summary(fit)$se