One step Tyler Shape Matrix

Description

This matrix can be used to get from ics the principal axes which is then known as principal axis analysis.

Usage

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covAxis(X, na.action = na.fail)

Arguments

X

numeric data matrix or dataframe.

na.action

a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

The covAxis matrix V is a given for a sample of size n as

p ave{[(x_i-x_bar)S^{-1}(x_i-x_bar)']^(-1) (x_i-x_bar)'(x_i-x_bar)},

where x_bar is the mean vector and S the regular covariance matrix.

covAxis can be used to perform a Prinzipal Axis Analysis (Critchley et al. 2006) using the function ics. In that case for a centered data matrix X covAxis can be used as S2 in ics, where S1 should be in that case the regular covariance matrix.

Value

Matrix of the estimated scatter.

Author(s)

Klaus Nordhausen

References

Critchley , F., Pires, A. and Amado, C. (2006), Principal axis analysis, Technical Report, 06/14, The Open University Milton Keynes.

Tyler, D.E., Critchley, F., Dümbgen, L. and Oja, H. (2009), Invariant co-ordinate selecetion, Journal of the Royal Statistical Society,Series B, 71, 549–592. <doi:10.1111/j.1467-9868.2009.00706.x>.

See Also

ics

Examples

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data(iris)
iris.centered <- sweep(iris[,1:4], 2, colMeans(iris[,1:4]), "-")
iris.paa <- ics(iris.centered, cov, covAxis, stdKurt = FALSE)
summary(iris.paa)
plot(iris.paa, col=as.numeric(iris[,5]))    
mean(iris.paa@gKurt)
emp.align <- iris.paa@gKurt
emp.align

screeplot(iris.paa)
abline(h = 1)