cov.rob {MASS} | R Documentation

## Resistant Estimation of Multivariate Location and Scatter

### Description

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.

### 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 enumeration is done up to 5000 samples: if `"exact"` exhaustive enumeration will be attempted however many samples are needed.
`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.

### Author(s)

B.D. Ripley

### 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

`lqs`

### Examples

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

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