# Robust covariance matrix estimation

### Description

Obtains a robust estimate of the covariance matrix of a sample of multivariate data, using Campbell's (1980) method as described on p231-235 of Krzanowski (1988).

### Usage

1 |

### Arguments

`sY` |
A matrix, where each column is a replicate observation on a multivariate r.v. |

`alpha` |
tuning parameter, see details. |

`beta` |
tuning parameter, see details. |

### Details

Campbell (1980) suggests an estimator of the covariance
matrix which downweights observations at more than some
Mahalanobis distance `d.0`

from the mean.
`d.0`

is `sqrt(nrow(sY))+alpha/sqrt(2)`

.
Weights are one for observations with Mahalanobis
distance, `d`

, less than `d.0`

. Otherwise
weights are `d.0*exp(-.5*(d-d.0)^2/beta)/d`

. The
defaults are as recommended by Campbell. This routine
also uses pre-conditioning to ensure good scaling and
stable numerical calculations.

### Value

A list where:

`E`

a square root of the inverse covariance matrix. i.e. the inverse cov matrix is`t(E)%*%E`

;`half.ldet.V`

Half the log of the determinant of the covariance matrix;`mY`

The estimated mean;`sd`

The estimated standard deviations of each variable.

### Author(s)

Simon N. Wood, maintained by Matteo Fasiolo <matteo.fasiolo@gmail.com>.

### References

Krzanowski, W.J. (1988) Principles of Multivariate Analysis. Oxford. Campbell, N.A. (1980) Robust procedures in multivariate analysis I: robust covariance estimation. JRSSC 29, 231-237.

### Examples

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