# testcoef.xenv: Hypothesis test of the coefficients of the predictor envelope... In Renvlp: Computing Envelope Estimators

## 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 predictor envelope model.

## Usage

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

## Arguments

 `m` A list containing estimators and other statistics inherited from xenv. `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 envelope model in predictor space. 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

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

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