# testcoef.stenv: Hypothesis test of the coefficients of the simultaneous... In Renvlp: Computing Envelope Estimators

 testcoef.stenv R Documentation

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

### Description

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

### Usage

```testcoef.stenv(m, L, R, A)
```

### Arguments

 `m` A list containing estimators and other statistics inherited from stenv. `L` The matrix multiplied to beta on the left. It is a d1 by p matrix, while d1 is less than or equal to p. `R` The matrix multiplied to beta on the right. It is an r by d2 matrix, while d2 is less than or equal to r. `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 beta R = A, versus Ha: L beta R != A. The beta is estimated by the simultaneous envelope model. If L = Ip, R = Ir and A = 0, then the test is equivalent to the standard F test on if beta = 0. The test statistic used is vec(L beta R - A) hatSigma^-1 vec(L beta R - A)^T, where beta is the envelope estimator and hatSigma is the estimated asymptotic covariance of vec(L beta 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 beta R).

### Examples

```data(fiberpaper)
X <- fiberpaper[ , 5:7]
Y <- fiberpaper[ , 1:4]
m <- stenv(X, Y, 2, 3)

L <- diag(3)
R <- as.matrix(c(1, 0, 0, 0), nrow = 4)
A <- matrix(0, 3, 1)

test.res <- testcoef.stenv(m, L, R, A)
test.res
```

Renvlp documentation built on Aug. 8, 2022, 1:06 a.m.