covW {ICS} | R Documentation |
One-step M-estimator
Description
Estimates the scatter matrix based on one-step M-estimator using mean and covariance matrix as starting point.
Usage
covW(X, na.action = na.fail, alpha = 1, cf = 1)
Arguments
X |
numeric |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
alpha |
parameter of the one-step M-estimator. By default equals to 1. |
cf |
consistency factor of the one-step M-estimator. By default equals to 1. |
Details
It is given for matrix
by
where is the mean vector,
is the squared
Mahalanobis distance,
is a
non-negative and continuous weight function and
is a consistency factor.
Note that the consistency factor, which makes the estimator consistent at the multivariate normal distribution, is in most case unknown and therefore the default is to use simply
cf = 1
.
If
, we get the covariance matrix
cov()
(up to the factorinstead of
).
If
, we get the
covAxis()
.If
, we get the
cov4()
with.
Value
A matrix containing the one-step M-scatter.
Author(s)
Aurore Archimbaud and Klaus Nordhausen
References
Archimbaud, A., Drmac, Z., Nordhausen, K., Radojicic, U. and Ruiz-Gazen, A. (2023). SIAM Journal on Mathematics of Data Science (SIMODS), Vol.5(1):97–121. doi:10.1137/22M1498759.
See Also
Examples
data(iris)
X <- iris[,1:4]
# Equivalence with covAxis
covW(X, alpha = -1, cf = ncol(X))
covAxis(X)
# Equivalence with cov4
covW(X, alpha = 1, cf = 1/(ncol(X)+2))
cov4(X)
# covW with alpha = 0.5
covW(X, alpha = 0.5)