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

 testcoef.penv R Documentation

## Hypothesis test of the coefficients of the partial envelope model

### 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

```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

```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 Jan. 8, 2023, 1:08 a.m.