covTest.single {MNormTest} | R Documentation |
Single Covariance Matrix Hypothesis Testing
Description
Test whether the covariance matrix is equal to a certain value. The null hypothesis is "H0: Sigma = Sigma0" or "H0: Sigma = sigma^2 * Sigma0".
Usage
covTest.single(data, Sigma0, ball = FALSE, alpha = 0.05, verbose = TRUE)
Arguments
data |
The data matrix which is a matrix or data frame. |
Sigma0 |
The covariance matrix when the null hypothesis is true. |
ball |
A boolean value. Default is FALSE. If FALSE, test whether the covariance matrix is Sigma0 (known), which means the null hypothesis is "H0: Sigma = Sigma0". If TRUE and the Sigma0 is a unit matrix, the Mauchly's ball test will be performed. If TRUE but Sigma0 (known) is not a unit matrix, the covariance matrix will be tested to see if it is sigma^2*Sigma0 (sigma^2 is unknown), which means the null hypothesis is "H0: Sigma = sigma^2 * Sigma0". |
alpha |
The significance level. Default is 0.05. |
verbose |
A boolean value. Default is TRUE. If TRUE, the null hypothesis will be displayed. If FALSE, the test will be carried out silently. |
Value
An object of class "testResult", which is a list with the following elements: Return when ball is FALSE.
Conclusion |
The conclusion of the test. |
Stat |
A data frame containing the statistics, p value and critical value. |
SampMean |
The sample mean. |
SampA |
The sample deviation. |
Df |
The degree of freedom. |
Return when ball is TRUE
Conclusion |
The conclusion of the test. |
Stat |
A data frame containing the statistics, p value and critical value. |
SampMean |
The sample mean. |
SampA |
The sample deviation. |
sigma.hat |
The estimation of sigma^2. |
Df |
The degree of freedom. |
Author(s)
Xifeng Zhang
References
Huixuan, Gao. Applied Multivariate Statistical Analysis. Peking University Press, 2005: pp.83-88.
Examples
data(iris)
X <- iris[, 1:4]
# carry out the test
test1 <- covTest.single(X, diag(1, 4))
test2 <- covTest.single(X, diag(1, 4), ball = TRUE)
test3 <- covTest.single(X, diag(2, 4), ball = TRUE)
test4 <- covTest.single(X, diag(1, 4), verbose = FALSE)
# get the elements
test1$Stat
test2$Df
test3$sigma.hat