ICtest (version 0.3-5)

PCAschott: Testing for Subsphericity using the Schott's test

Description

The test tests the equality of the last eigenvalues assuming normal distributed data using the regular covariance matrix.

Usage

PCAschott(X, k)

Arguments

X

a numeric data matrix with p>1 columns.

k

the number of eigenvalues larger than the equal ones. Can be between 0 and p-2.

Value

A list of class ictest inheriting from class htest containing:

statistic

the value of the test statistic.

p.value

the p-value of the test.

parameter

the degrees of freedom of the test.

method

character string which test was performed.

data.name

character string giving the name of the data.

alternative

character string specifying the alternative hypothesis.

k

the number or larger eigenvalues used in the testing problem.

W

the transformation matrix to the principal components.

S

data matrix with the centered principal components.

D

the underlying eigenvalues.

MU

the mean vector of the data which was substracted before calculating the principal components.

SCATTER

the computed covariance matrix matrix.

Details

The functions assumes multivariate normal data and tests if the last \(p-k\) eigenvalues of PCA are equal.

References

Schott, J.R. (2006), A High-Dimensional Test for the Equality of the Smallest Eigenvalues of a Covariance Matrix, Journal of Multivariate Analysis, 97, 827--843. <doi:10.1016/j.jmva.2005.05.003>

See Also

PCAasymp, PCAboot

Examples

# NOT RUN {
n <- 200
X <- cbind(rnorm(n, sd = 2), rnorm(n, sd = 1.5), rnorm(n), rnorm(n), rnorm(n))
PCAschott(X, 2)
# }