Sest_multireg {FRB} | R Documentation |
Computes S-Estimates of multivariate regression based on Tukey's biweight function using the fast-S algorithm.
Sest_multireg(X, Y, bdp = 0.5, control=Scontrol(...), ...)
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 |
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.
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 |
w |
implicit weights corresponding to the S-estimates (i.e. final weights in the RWLS procedure at the end of the fast-S algorithm) |
outFlag |
outlier flags: 1 if the robust distance of the residual exceeds the .975 quantile of (the square root of) the chi-square distribution with degrees of freedom equal to the dimension of the responses; 0 otherwise |
Gert Willems and Ella Roelant
FRBmultiregS
, Sboot_multireg
, MMest_multireg
, Scontrol
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$Beta n <- nrow(school.x) par(mfrow=c(2,1)) # the estimates can be considered as weighted least squares estimates with the # following implicit weights plot(1:n, Sres$w) # Sres$outFlag tells which points are outliers based on whether or not their # robust distance exceeds the .975 chi-square cut-off: plot(1:n, Sres$outFlag) # (see also the diagnostic plot in plotDiag())