| PCAschott {ICtest} | R Documentation |
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. |
Details
The functions assumes multivariate normal data and tests if the last p-k eigenvalues of PCA are equal.
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. |
Author(s)
Klaus Nordhausen
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
Examples
n <- 200
X <- cbind(rnorm(n, sd = 2), rnorm(n, sd = 1.5), rnorm(n), rnorm(n), rnorm(n))
PCAschott(X, 2)