Description Usage Arguments Details Value Author(s) References Examples
Obtains a robust estimate of the covariance matrix of a sample of multivariate data, using Campbell's (1980) method as described on p231-235 of Krzanowski (1988).
1 |
sY |
A matrix, where each column is a replicate observation on a multivariate r.v. |
alpha |
tuning parameter, see details. |
beta |
tuning parameter, see details. |
Campbell (1980) suggests an estimator of the covariance
matrix which downweights observations at more than some
Mahalanobis distance d.0
from the mean.
d.0
is sqrt(nrow(sY))+alpha/sqrt(2)
.
Weights are one for observations with Mahalanobis
distance, d
, less than d.0
. Otherwise
weights are d.0*exp(-.5*(d-d.0)^2/beta)/d
. The
defaults are as recommended by Campbell. This routine
also uses pre-conditioning to ensure good scaling and
stable numerical calculations.
A list where:
E
a square root of
the inverse covariance matrix. i.e. the inverse cov
matrix is t(E)%*%E
;
half.ldet.V
Half the log of the determinant
of the covariance matrix;
mY
The estimated
mean;
sd
The estimated standard deviations
of each variable.
Simon N. Wood, maintained by Matteo Fasiolo <matteo.fasiolo@gmail.com>.
Krzanowski, W.J. (1988) Principles of Multivariate Analysis. Oxford. Campbell, N.A. (1980) Robust procedures in multivariate analysis I: robust covariance estimation. JRSSC 29, 231-237.
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