MMest_loccov {FRB} | R Documentation |
Computes MM-estimates of multivariate location and covariance, using an initial S-estimate
MMest_loccov(Y, control=MMcontrol(...), ...)
Y |
matrix or data frame |
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 FRBpcaMM
and FRBhotellingMM
.
The MM-estimates are defined by first computing S-estimates of location and covariance, then fixing the scale component and
re-estimating the location and shape by more efficient M-estimates (see Tatsuoka and Tyler (2000)). 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.
This tuning can be changed via argument control
if desired.
When interested in location estimates, control parameter shapeEff
should be FALSE
(the default),
in which case the particular efficiency is that of the location estimate. When interest lies in the covariance or shape part, e.g. in PCA analysis,
it makes sense to set shapeEff=TRUE
, in which case the shape efficiency is considered instead.
The computation of the S-estimates is performed by a call to Sest_loccov
, which uses the fast-S algorithm.
See MMcontrol
() to see or change the tuning parameters for this algorithm.
Apart from the MM-location estimate Mu
, the function returns both the MM-covariance Sigma
and MM-shape estimate Gamma
(which has determinant equal to 1).
Additionally, the 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:
Mu |
MM-estimate of location |
Sigma |
MM-estimate of covariance |
Gamma |
MM-estimate of shape |
SMu |
S-estimate of location |
SSigma |
S-estimate of covariance |
SGamma |
S-estimate of shape |
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
Sest_loccov
, FRBpcaMM
, FRBhotellingMM
,
MMboot_loccov
, MMcontrol
Y <- matrix(rnorm(50*5), ncol=5) MMests <- MMest_loccov(Y) # MM-estimate of location: MMests$Mu # MM-estimate of covariance: MMests$Sigma # initial S-estimate of location: MMests$SMu