covAxis: One step Tyler Shape Matrix

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

Usage

1

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)

ICS documentation built on May 29, 2017, 6:12 p.m.

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