GSest_multireg {FRB} | R Documentation |
Computes GS-Estimates of multivariate regression based on Tukey's biweight function.
GSest_multireg(X, Y, bdp = 0.5, control=GScontrol(...), ...)
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 . |
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.
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 |
Ella Roelant and Gert Willems
FRBmultiregGS
, GSboot_multireg
, Sest_multireg
, GScontrol
data(schooldata) school.x <- data.matrix(schooldata[,1:5]) school.y <- data.matrix(schooldata[,6:8]) GSest <- GSest_multireg(school.x,school.y)