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Does anyone knows if there exists an implementation of the minimum covariance determinant estimate (MCD) to the spread of multivariate data. This method was developed by Rousseeuw (1984) and there exists implementations in many if not all statistical packages (R, Matlab, SAS, etc.).

Surprisingly, I seem to be unable to find an implementation for Mathematica.

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Because there was no answer, I chose to implement the function myself. The following notebook contains a litteral implementation of the algorithm found in

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

The only addition is the Consistency-to-normal-model factor; see

Pison, G., Van Aelst, S., & Willems, G. (2002) Small sample corrections for LTS and MCD. Metrika (2002) 55: 111. doi:10.1007/s001840200191

This factor makes the estimate comparable to the variance-covariance matrix of the full data set if there was not contaminant and the population was truly normal.

The notebook can be found at MCD.nb. It is distributed without no warranty. For small samples,it was compared with the R implementation of the algorithm and the results were identical. If you spot problems, let me know.

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