covAxis | R Documentation |

This matrix can be used to get the principal axes from `ics`

,
which is then known as principal axis analysis.

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

`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. |

The `covAxis`

matrix `V`

is a given for a `n \times p`

data matrix X as

`p \ ave_{i}\{[(x_{i}-\bar{x})S^{-1}(x_{i}-\bar{x})']^{-1}(x_{i}-\bar{x})'(x_{i}-\bar{x})\},`

where `\bar{x}`

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.

A matrix containing the estimated one step Tyler shape matrix.

Klaus Nordhausen

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., D?mbgen, 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>.

`ics`

```
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)
```

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