ch99AsymptoticDF {CerioliOutlierDetection} R Documentation

## Croux and Haesbroeck (1999) finite-sample asymptotic approximation parameters for the MCD estimate

### Description

Computes the asymptotic Wishart degrees of freedom and consistency constant for the MCD robust dispersion estimate (for data with a model normal distribution) as described in Hardin and Rocke (2005) and using the formulas described in Croux and Haesbroeck (1999).

### Usage

```ch99AsymptoticDF(n.obs, p.dim, mcd.alpha)
```

### Arguments

 `n.obs` (Integer) Number of observations `p.dim` (Integer) Dimension of the data, i.e., number of variables. `mcd.alpha` (Numeric) Value that determines the fraction of the sample used to compute the MCD estimate. 1 - mcd.alpha will be the fraction of observations that are omitted in computing the MCD estimate. The default value is \lfloor (n.obs + p.dim + 1)/2 \rfloor/n.obs, which yields the MCD estimate with the maximum possible breakdown point.

### Details

The consistency factor `c.alpha` is already available in the `robustbase` library as the function `.MCDcons`. (See the code for `covMcd`.) `ch99AsymptoticDF` uses the result of `.MCDcons` for consistency.

The computation of the asymptotic Wishart degrees of freedom parameter `m` follows the Appendix of Hardin and Rocke (2005).

### Value

 `c.alpha` the asymptotic consistency coefficient for the MCD estimate of the dispersion matrix `m.hat.asy` the asymptotic degrees of freedom for the Wishart distribution approximation to the distribution of the MCD dispersion estimate

### Author(s)

Written and maintained by Christopher G. Green <christopher.g.green@gmail.com>

### References

Christopher Croux and Gentiane Haesbroeck. Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis, 71:161-190, 1999. doi: 10.1006/jmva.1999.1839

J. Hardin and D. M. Rocke. The distribution of robust distances. Journal of Computational and Graphical Statistics, 14:928-946, 2005. doi: 10.1198/106186005X77685

### Examples

```# compare to table from p941 of Hardin and Rocke (2005)
ch99AsymptoticDF(  50, 5)
ch99AsymptoticDF( 100,10)
ch99AsymptoticDF( 500,10)
ch99AsymptoticDF(1000,20)
```

[Package CerioliOutlierDetection version 1.1.9 Index]