GSest_multireg {FRB}R Documentation

GS Estimates for Multivariate Regression

Description

Computes GS-Estimates of multivariate regression based on Tukey's biweight function.

Usage

GSest_multireg(X, Y, bdp = 0.5, control=GScontrol(...), ...)

Arguments

X a matrix or data frame containing the explanatory variables.
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 GScontrol().
... allows for specifying control parameters directly instead of via control.

Details

Called by FRBmultiregGS and typically not to be used on its own.

Generalized S-estimators are defined by minimizing the determinant of a robust estimator of the scatter matrix of the differences of the residuals. Hence, this procedure is intercept free and only gives an estimate for the slope matrix. To estimate the intercept, we use the M-type estimator of location of Lopuhaa (1992) on the residuals with the residual scatter matrix estimate of the residuals as a preliminary estimate. We use a fast algorithm similar to the one proposed by Salibian-Barrera and Yohai (2006) for the regression case. See GScontrol for the adjustable tuning parameters of this algorithm.

Value

A list containing the following components:

Beta GS-estimate of the regression coefficient matrix (including the intercept)
Gamma GS-estimate of the error shape matrix
Sigma GS-estimate of the error covariance matrix
scale GS-estimate of the error scale (univariate)
b,c tuning parameters used in Tukey biweight loss function, as determined by bdp

Author(s)

Ella Roelant and Gert Willems

References

See Also

FRBmultiregGS, GSboot_multireg, Sest_multireg, GScontrol

Examples

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

[Package FRB version 1.4 Index]