MMest_multireg {FRB}R Documentation

MM-Estimates for Multivariate Regression

Description

Computes MM-Estimates of multivariate regression, using initial S-estimates

Usage

MMest_multireg(X, Y, control=MMcontrol(...), ...)

Arguments

X a matrix or data frame containing the explanatory variables (possibly including intercept).
Y a matrix or data frame containing the response variables.
control a list with control parameters for tuning the MM-estimate and its computing algorithm, see MMcontrol().
... allows for specifying control parameters directly instead of via control

Details

This function is called by FRBmultiregMM.

The MM-estimates are defined by first computing S-estimates of regression, then fixing the scale component of the error covariance estimate, and finally re-estimating the regression coefficients and the shape part of the error covariance by more efficient M-estimates (see Tatsuoka and Tyler (2000) for MM-estimates in the special case of location/scatter estimation, and Van Aelst and Willems (2005) for S-estimates of multivariate regression). Tukey's biweight is used for the loss functions. By default, the first loss function (in the S-estimates) is tuned in order to obtain 50% breakdown point. The default tuning of the second loss function (M-estimates) ensures 95% efficiency at the normal model for the coefficient estimates. This tuning can be changed via argument control if desired.

The computation of the S-estimates is performed by a call to Sest_multireg, which uses the fast-S algorithm. See MMcontrol() to see or change the tuning parameters for this algorithm.

Apart from the MM-estimate of the regression coefficients Beta, the function returns both the MM-estimate of the error covariance Sigma and the corresponding shape estimate Gamma (which has determinant equal to 1). Additionally, the initial S-estimates are returned as well (their Gaussian efficiency is usually lower than the MM-estimates but they may have a lower bias).

Value

A list containing:

Beta MM-estimate of the regression coefficient matrix
Sigma MM-estimate of the error covariance matrix
Gamma MM-estimate of the error shape matrix
SBeta S-estimate of the regression coefficient matrix
SSigma S-estimate of the error covariance matrix
SGamma S-estimate of the error shape matrix
scale S-estimate of scale (univariate)
c0,b,c1 tuning parameters of the loss functions (depend on control parameters bdp and eff)

Author(s)

Gert Willems and Ella Roelant

References

See Also

FRBmultiregMM, MMboot_multireg, Sest_multireg, MMcontrol

Examples

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

# compute 25% breakdown S-estimates
MMres <- MMest_multireg(school.x,school.y)
# the MM-estimate of the regression coefficient matrix:
MMres$Beta

[Package FRB version 1.4 Index]