ch99AsymptoticDF | R Documentation |
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).
ch99AsymptoticDF(n.obs, p.dim, mcd.alpha)
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.
which yields the MCD estimate with the maximum possible breakdown point. |
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).
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 |
Written and maintained by Christopher G. Green <christopher.g.green@gmail.com>
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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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)
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