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Fri Oct 8 09:07:10 2004 UTC (10 years, 3 months ago) by
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Original Path:
trunk/physics/inc/TRobustEstimator.h
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From Anna Kreshuk
New class TRobustEstimator
// TRobustEstimator
//
// Minimum Covariance Determinant Estimator - a Fast Algorithm
// invented by Peter J.Rousseeuw and Katrien Van Dreissen
// "A Fast Algorithm for the Minimum covariance Determinant Estimator"
// Technometrics, August 1999, Vol.41, NO.3
//
// What are robust estimators?
// "An important property of an estimator is its robustness. An estimator
// is called robust if it is insensitive to measurements that deviate
// from the expected behaviour. There are 2 ways to treat such deviating
// measurements: one may either try to recongize them and then remove
// them from the data sample; or one may leave them in the sample, taking
// care that they do not influence the estimate unduly. In both cases robust
// estimators are needed...Robust procedures compensate for systematic errors
// as much as possible, and indicate any situation in which a danger of not being
// able to operate reliably is detected."
// R.Fruhwirth, M.Regler, R.K.Bock, H.Grote, D.Notz
// "Data Analysis Techniques for High-Energy Physics", 2nd edition
//
// What does this algorithm do?
// It computes a highly robust estimator of multivariate location and scatter.
// Then, it takes those estimates to compute robust distances of all the
// data vectors. Those with large robust distances are considered outliers.
// Robust distances can then be plotted for better visualization of the data.
//
// How does this algorithm do it?
// The MCD objective is to find h observations(out of n) whose classical
// covariance matrix has the lowest determinant. The MCD estimator of location
// is then the average of those h points and the MCD estimate of scatter
// is their covariance matrix. The minimum(and default) h = (n+nvariables+1)/2
// so the algorithm is effective when less than (n+nvar+1)/2 variables are outliers.
// The algorithm also allows for exact fit situations - that is, when h or more
// observations lie on a hyperplane. Then the algorithm still yields the MCD location T
// and scatter matrix S, the latter being singular as it should be. From (T,S) the
// program then computes the equation of the hyperplane.
//
// How can this algorithm be used?
// In any case, when contamination of data is suspected, that might influence
// the classical estimates.
// Also, robust estimation of location and scatter is a tool to robustify
// other multivariate techniques such as, for example, principal-component analysis
// and discriminant analysis.
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