# 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

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

1 2 3 4 5 6 7 8 9 10 11 |