### Highlights from LMS Toolbox

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# LMS Toolbox

### Alexandros Leontitsis (view profile)

27 Sep 2001 (Updated )

Least median of squares regression and relative algorithms

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Description

This toolbox contains a set of functions which can be used to compute the Least Median of Squares regression, the Reweighted Least Squares regression, the accociated location and scale estiamtors, and the Minimum Volume Ellipsoid. The concept is the minimization of the median of the squared errors (residuals) in order to achieve robustness against the outliers.

Acknowledgements
MATLAB release MATLAB 6.5 (R13)
07 Apr 2007 k elmurapet
15 Feb 2006 Min Poh

Well documented with working functions.

06 Oct 2004 David Sterling

There are three problems with the MVE routine (the only one I've looked at so far).

The most serious problem is a bug on line 68:
vol=sqrt(det(Cj))*mj^(p-1);
vol=sqrt(det(Cj))*mj^(p);
according to eq 1.25 in Rousseau and Leroy, "Robust Regression and Outlier Detection", Wiley 2003.

Another problem is that the routine was apparently written with "small" data sets in mind since it performs an exhaustive (combinatorial) search of all nchoosek(n,p+1)
permutations given by:

C=combnk(1:n,p+1);

This can be an extremely large number of combinations for moderate two dimensional data sets. See Rousseau and Leroy above for alternatives.

A final comment about effeciency: the routine several "for" loops that can easily be replaced by Matlab's "vectorized" operations which are more efficient.

05 Apr 2004 Fred Webber

The algorithms implemented in these programs are not the best that are available. See http://www.agoras.ua.ac.be/

Rousseeuw, P.J. and Van Driessen, K. (1999), A Fast Algorithm for the Minimum Covariance Determinant Estimator, Technometrics, 41, 212-223.
Abstract - Program FAST-MCD - Program FAST-MCD IN MATLAB - Paper

Rousseeuw, P.J. and Van Driessen, K. (1999), Computing LTS Regression for Large Data Sets, Technical Report, University of Antwerp, submitted.
Abstract - Program FAST-LTS - Program FAST-LTS IN MATLAB - Paper

Comment only
24 Jun 2003 David Sharim
19 Oct 2002
04 Oct 2001

bug fix

05 Oct 2001

performance improvement

09 Oct 2001

bug fix

19 Jan 2002

LMSar function bug fix