tcov {ICSClust} | R Documentation |
Pairwise one-step M-estimate of scatter
Description
Computes a pairwise one-step M-estimate of scatter with weights based on pairwise Mahalanobis distances. Note that it is based on pairwise differences and therefore does not require a location estimate.
Usage
tcov(x, beta = 2)
Arguments
x |
a numeric matrix or data frame. |
beta |
a positive numeric value specifying the tuning parameter of the pairwise one-step M-estimator (defaults to 2), see ‘Details’. |
Details
For a sample , a positive and decreasing weight function
,
and a tuning parameter
, the pairwise one-step M-estimator
of scatter is defined as
where
denotes the squared pairwise Mahalanobis distance between observations
and
based on the sample
covariance matrix
. Here, the weight
function
is used.
Value
A numeric matrix giving the pairwise one-step M-estimate of scatter.
Author(s)
Andreas Alfons and Aurore Archimbaud
References
Caussinus, H. and Ruiz-Gazen, A. (1993) Projection Pursuit and Generalized Principal Component Analysis. In Morgenthaler, S., Ronchetti, E., Stahel, W.A. (eds.) New Directions in Statistical Data Analysis and Robustness, 35-46. Monte Verita, Proceedings of the Centro Stefano Franciscini Ascona Series. Springer-Verlag.
Caussinus, H. and Ruiz-Gazen, A. (1995) Metrics for Finding Typical Structures by Means of Principal Component Analysis. In Data Science and its Applications, 177-192. Academic Press.
See Also
ICS_tcov()
, ucov()
, ICS_ucov()