testcoef.penv: Hypothesis test of the coefficients of the partial envelope...

In therimalaya/envelope: Computing Envelope Estimators in Multivariate Linear Regression

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, and 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 statistics.
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

therimalaya/envelope documentation built on May 29, 2019, 1:38 p.m.