# MM Estimates of Multivariate Location and Scatter

### Description

Computes MM-Estimates of multivariate location and scatter starting from an initial S-estimate

### Usage

1 2 |

### Arguments

`x` |
a matrix or data frame. |

`bdp` |
a numeric value specifying the required
breakdown point. Allowed values are between
0.5 and 1 and the default is |

`eff` |
a numeric value specifying the required efficiency
for the MM estimates. Default is |

`eff.shape` |
logical; if TRUE, eff is with regard to shape-efficiency, otherwise location-efficiency. Default is |

`maxiter` |
maximum number of iterations allowed
in the computation of the S-estimate (bisquare and Rocke type).
Default is |

`trace` |
whether to print intermediate results. Default is |

`tolSolve` |
numeric tolerance to be used as a convergence tolerance for the MM-iteration |

`control` |
a control object (S4) of class |

### Details

Computes MM-estimates of multivariate location and scatter starting from an initial S-estimate.

### Value

An S4 object of class `CovMMest-class`

which is a subclass of the
virtual class `CovRobust-class`

.

### Author(s)

Valentin Todorov valentin.todorov@chello.at

### References

Tatsuoka, K.S. and Tyler, D.E. (2000).
The uniqueness of S and M-functionals under non-elliptical distributions.
*Annals of Statistics* 28, 1219–1243

M. Salibian-Barrera, S. Van Aelstt and G. Willems (2006).
Principal components analysis based on multivariate MM-estimators with fast and robust bootstrap.
*Journal of the American Statistical Association* 101, 1198–1211.

R. A. Maronna, D. Martin and V. Yohai (2006).
*Robust Statistics: Theory and Methods*.
Wiley, New York.

Todorov V & Filzmoser P (2009),
An Object Oriented Framework for Robust Multivariate Analysis.
*Journal of Statistical Software*, **32**(3), 1–47.
URL http://www.jstatsoft.org/v32/i03/.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
library(rrcov)
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovMMest(hbk.x)
## the following four statements are equivalent
c0 <- CovMMest(hbk.x)
c1 <- CovMMest(hbk.x, bdp = 0.25)
c2 <- CovMMest(hbk.x, control = CovControlMMest(bdp = 0.25))
c3 <- CovMMest(hbk.x, control = new("CovControlMMest", bdp = 0.25))
## direct specification overrides control one:
c4 <- CovMMest(hbk.x, bdp = 0.40,
control = CovControlMMest(bdp = 0.25))
c1
summary(c1)
plot(c1)
## Deterministic MM-estmates
CovMMest(hbk.x, control=CovControlMMest(sest=CovControlSest(method="sdet")))
``` |