# testcoef.penv: Hypothesis test of the coefficients of the partial envelope... In Renvlp: Computing Envelope Estimators

## Description

This function tests the null hypothesis L * beta1 * R = A versus the alternative hypothesis L * beta1 * R ~= A, where beta is estimated under the partial envelope model.

## Usage

 `1` ```testcoef.penv(m, L, R, A) ```

## Arguments

 `m` A list containing estimators and other statistics inherited from penv. `L` The matrix multiplied to beta on the left. It is a d1 by r matrix, while d1 is less than or equal to r. `R` The matrix multiplied to beta on the right. It is a p1 by d2 matrix, while d2 is less than or equal to p1. `A` The matrix on the right hand side of the equation. It is a d1 by d2 matrix.

Note that inputs `L`, `R` and `A` must be matrices, if not, use `as.matrix` to convert them.

## Details

This function tests for hypothesis H0: L beta1 R = A, versus Ha: L beta1 R != A. The beta is estimated by the partial envelope model. If L = Ir, R = Ip1 and A = 0, then the test is equivalent to the standard F test on if beta1 = 0. The test statistics used is vec(L beta1 R - A) hatSigma^-1 vec(L beta1 R - A)^T, where beta is the envelope estimator and hatSigma is the estimated asymptotic covariance of vec(L beta1 R - A). The reference distribution is chi-squared distribution with degrees of freedom d1 * d2.

## Value

The output is a list that contains following components.

 `chisqStatistic` The test statistic. `dof` The degrees of freedom of the reference chi-squared distribution. `pValue` p-value of the test. `covMatrix` The covariance matrix of vec(L beta1 R).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```data(fiberpaper) X1 <- fiberpaper[, 7] X2 <- fiberpaper[, 5:6] Y <- fiberpaper[, 1:4] m <- penv(X1, X2, Y, 1) m L <- diag(4) R <- as.matrix(1) A <- matrix(0, 4, 1) test.res <- testcoef.penv(m, L, R, A) test.res ```

Renvlp documentation built on Sept. 11, 2021, 9:07 a.m.