# cov.rob

##### Resistant Estimation of Multivariate Location and Scatter

Compute a multivariate location and scale estimate with a high
breakdown point -- this can be thought of as estimating the mean and
covariance of the `good`

part of the data. `cov.mve`

and
`cov.mcd`

are compatibility wrappers.

- Keywords
- multivariate, robust

##### Usage

```
cov.rob(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
method = c("mve", "mcd", "classical"),
nsamp = "best", seed)
```cov.mve(...)
cov.mcd(...)

##### Arguments

- x
- a matrix or data frame.
- cor
- should the returned result include a correlation matrix?
- quantile.used
- the minimum number of the data points regarded as
`good`

points. - method
- the method to be used -- minimum volume ellipsoid, minimum
covariance determinant or classical product-moment. Using
`cov.mve`

or`cov.mcd`

forces`mve`

or`mcd`

respectively. - nsamp
- the number of samples or
`"best"`

or`"exact"`

or`"sample"`

. If`"sample"`

the number chosen is`min(5*p, 3000)`

, taken from Rousseeuw and Hubert (1997). If`"best"`

exhaustive - seed
- the seed to be used for random sampling: see
`RNGkind`

. The current value of`.Random.seed`

will be preserved if it is set. - ...
- arguments to
`cov.rob`

other than`method`

.

##### Details

For method `"mve"`

, an approximate search is made of a subset of
size `quantile.used`

with an enclosing ellipsoid of smallest volume; in
method `"mcd"`

it is the volume of the Gaussian confidence
ellipsoid, equivalently the determinant of the classical covariance
matrix, that is minimized. The mean of the subset provides a first
estimate of the location, and the rescaled covariance matrix a first
estimate of scatter. The Mahalanobis distances of all the points from
the location estimate for this covariance matrix are calculated, and
those points within the 97.5% point under Gaussian assumptions are
declared to be `good`

. The final estimates are the mean and rescaled
covariance of the `good`

points.

The rescaling is by the appropriate percentile under Gaussian data; in
addition the first covariance matrix has an *ad hoc* finite-sample
correction given by Marazzi.

For method `"mve"`

the search is made over ellipsoids determined
by the covariance matrix of `p`

of the data points. For method
`"mcd"`

an additional improvement step suggested by Rousseeuw and
van Driessen (1999) is used, in which once a subset of size
`quantile.used`

is selected, an ellipsoid based on its covariance
is tested (as this will have no larger a determinant, and may be smaller).

##### Value

- A list with components
center the final estimate of location. cov the final estimate of scatter. cor (only is `cor = TRUE`

) the estimate of the correlation matrix.sing message giving number of singular samples out of total crit the value of the criterion on log scale. For MCD this is the determinant, and for MVE it is proportional to the volume. best the subset used. For MVE the best sample, for MCD the best set of size `quantile.used`

.n.obs total number of observations.

##### References

P. J. Rousseeuw and A. M. Leroy (1987)
*Robust Regression and Outlier Detection.*
Wiley.

A. Marazzi (1993)
*Algorithms, Routines and S Functions for Robust Statistics.*
Wadsworth and Brooks/Cole.

P. J. Rousseeuw and B. C. van Zomeren (1990) Unmasking
multivariate outliers and leverage points,
*Journal of the American Statistical Association*, **85**, 633--639.

P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the
minimum covariance determinant estimator. *Technometrics*
**41**, 212--223.

P. Rousseeuw and M. Hubert (1997) Recent developments in PROGRESS. In
*L1-Statistical Procedures and Related Topics*
ed Y. Dodge, IMS Lecture Notes volume **31**, pp. 201--214.

##### See Also

##### Examples

```
set.seed(123)
cov.rob(stackloss)
cov.rob(stack.x, method = "mcd", nsamp = "exact")
```

*Documentation reproduced from package MASS, version 7.3-0, License: GPL-2 | GPL-3*