R: One step Tyler Shape Matrix

covAxis {ICS} | R Documentation

## 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

    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

    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)

[Package ICS version 1.3-0 Index]