Tenv_Pval {TRES}

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

## 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)