MMest_loccov {FRB}R Documentation

MM-Estimates of Location and Covariance

Description

Computes MM-estimates of multivariate location and covariance, using an initial S-estimate

Usage

MMest_loccov(Y, control=MMcontrol(...), ...)

Arguments

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

Details

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).

Value

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)

Author(s)

Gert Willems and Ella Roelant

References

See Also

Sest_loccov, FRBpcaMM, FRBhotellingMM, MMboot_loccov, MMcontrol

Examples

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


[Package FRB version 1.4 Index]