Sest_loccov {FRB}R Documentation

S-estimates of location/covariance

Description

Computes S-estimates of multivariate location and covariance using the fast-S algorithm

Usage

Sest_loccov(Y, bdp = 0.5, control=Scontrol(...), ...)

Arguments

Y matrix or data frame
bdp required breakdown point of the S-estimate. Should have 0 < bdp <= 0.5, the default is 0.5.
control a list with control parameters for tuning the computing algorithm, see Scontrol().
... allows for specifying control parameters directly instead of via control

Details

This function is called by FRBpcaS and FRBhotellingS.

Multivariate S-estimates were introduced by Davies (1987). The algorithm used here is a multivariate version of the fast-S algorithm introduced by Salibian-Barrera and Yohai (2006). See Scontrol for the adjustable tuning parameters of this algorithm.

The function both returns the covariance estimate Sigma and shape estimate Gamma (which has determinant equal to 1). The scale is determined by det(Sigma)^{1/2/p}, with p the number of variables.

Value

A list containing:

Mu S-estimate of location
Gamma S-estimate of shape
Sigma S-estimate of covariance
scale S-estimate of scale (univariate)
b,c tuning parameters used in Tukey biweight loss function, as determined by bdp

Author(s)

Gert Willems and Ella Roelant

References

See Also

FRBpcaS, FRBhotellingS, Sboot_loccov, MMest_loccov, Scontrol

Examples

Y <- matrix(rnorm(50*5), ncol=5)
Sests <- Sest_loccov(Y, bdp = 0.25) 
# S-estimate of location:
Sests$Mu
# S-estimate of covariance:
Sests$Sigma


[Package FRB version 1.4 Index]