LMS Toolbox

Least median of squares regression and relative algorithms

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.

• MATLAB release: MATLAB 6.5 (R13)

 

[David Sharim]

 

[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

[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);
should read:
      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.

[Min Poh]

Well documented with working functions.

[k elmurapet]