# Fully Efficient Robust Correlation Estimation

### Description

Calculates a robust and asymptotically fully efficient correlation matrix, see Gervini (2003) for details.

### Usage

1 | ```
Corefw(data, boundq = 0.975, startestimator = "wMCD")
``` |

### Arguments

`data` |
matrix with the observations in rows. |

`boundq` |
quantile-bound for comparism of theoretical and empirical distribution function, see details. |

`startestimator` |
start estimator to be used: |

### Details

This implementation calculates the (asymptotically) fully efficient scatter estimator proposed by Gervini (2003). Based on a an initial scatter estimator which can be determined by `startestimator`

residuals and their cumulative distribution function are calculated. This empirical distribution is compared with the theoretical one (a chisquare distribution). Only if the empirical distribution function lays under the theoretic one, from the `boundq`

-quantile onwords, observations are identified as outliers, the number depends on the distance between the distribution functions. Based on all observations which are not marked as outliers, the usual correlation is returned.

This procedure has asymptotically the same efficiency as the usual empirical correlation and retains the breakdown point of the initial scale estimator.

### Value

Numeric correlation matrix.

### Author(s)

Alexander Dürre

### References

Gervini, D. (2003): A robust and efficient adaptive reweighted estimator of multivariate location and scatter, *Journal of multivariate analysis*, vol 84, 116–144.

### Examples

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