ch99AsymptoticDF: 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)
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
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.
Author
Written and maintained by Christopher G. Green <christopher.g.green@gmail.com>
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).
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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1198/106186005X77685")
# compare to table from p941 of Hardin and Rocke (2005)ch99AsymptoticDF( 50, 5)
ch99AsymptoticDF( 100,10)
ch99AsymptoticDF( 500,10)
ch99AsymptoticDF(1000,20)