TRES (version 1.1.5)

Tenv_Pval: The \(p\)-value and standard error of coefficient in tensor response regression (TRR) model.

Description

Obtain \(p\)-value of each element in the tensor regression coefficient estimator. Two-sided t-tests are implemented on the coefficient estimator, where asymptotic covariance of the OLS estimator is used.

Usage

Tenv_Pval(x, y, Bhat)

Arguments

x

The response tensor instance \( r_1\times r_2\times \cdots \times r_m\).

y

A vector predictor of dimension \(p\).

Bhat

The estimator of tensor regression coefficient.

The \(p\)-value and the standard error of estimated coefficient are not provided for tensor predictor regression since they depend on \(\widehat{\mathrm{cov}}^{-1}\{\mathrm{vec}(\mathbf{X})\}\) which is unavailable due to the ultra-high dimension of \(\mathrm{vec}(\mathbf{X})\).

Value

p_ols

The p-value tensor of OLS estimator.

p_val

The p-value tensor of Bhat.

se

The standard error tensor of Bhat.

Examples

# NOT RUN {
## Use dataset bat
data("bat")
x <- bat$x
y <- bat$y
fit_std <- TRR.fit(x, y, method="standard")
Tenv_Pval(x, y, fit_std$coefficients)

# }