ch99AsymptoticDF {CerioliOutlierDetection}

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 <[e-mail]>

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)