# Tenv_Pval: The p-value and standard error of coefficient in tensor... In TRES: Tensor Regression with Envelope Structure and Three Generic Envelope Estimation Approaches

## 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

 1 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

 1 2 3 4 5 6 ## 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) 

TRES documentation built on Jan. 13, 2021, 7:59 p.m.