Sest_multireg {FRB}R Documentation

S-Estimates for Multivariate Regression

Description

Computes S-Estimates of multivariate regression based on Tukey's biweight function using the fast-S algorithm.

Usage

Sest_multireg(X, Y, bdp = 0.5, control=Scontrol(...), ...)

Arguments

X a matrix or data frame containing the explanatory variables (possibly including intercept).
Y a matrix or data frame containing the response variables.
bdp required breakdown point. 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 FRBmultiregS.

S-estimates for multivariate regression were discussed in Van Aelst and Willems (2005). 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.

Apart from the regression coefficients Beta, the function both returns the error covariance matrix estimate Sigma and the corresponding shape estimate Gamma (which has determinant equal to 1). The scale is determined by det(Sigma)^{1/2/q}, with q the number of response variables.

Value

Beta S-estimate of the regression coefficient matrix
Gamma S-estimate of the error shape matrix
Sigma S-estimate of the error covariance matrix
scale S-estimate of the error 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

FRBmultiregS, Sboot_multireg, MMest_multireg, Scontrol

Examples

data(schooldata)
school.x <- data.matrix(schooldata[,1:5])
school.y <- data.matrix(schooldata[,6:8])

# compute 25% breakdown S-estimates
Sres <- Sest_multireg(school.x,school.y, bdp=0.25)
# the regression coefficients:
Sres$Beta

[Package FRB version 1.4 Index]