MMest_multireg {FRB} | R Documentation |
Computes MM-Estimates of multivariate regression, using initial S-estimates
MMest_multireg(X, Y, control=MMcontrol(...), ...)
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 |
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).
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 ) |
Gert Willems and Ella Roelant
FRBmultiregMM
, MMboot_multireg
, Sest_multireg
, MMcontrol
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