Log of /trunk/math/physics/src/TRobustEstimator.cxx
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Modified
Thu Oct 15 16:33:04 2009 UTC (5 years, 3 months ago) by
brun
File length: 41411 byte(s)
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From Matthew Strait:
This patch fixes the spelling of "function" in the root source code
and documentation, which is misspelled (sometimes as part of larger
"function"-based words) at least 152 times:
* "funciton" 48 times
* "funcion" 36 times
* "funtion" 23 times
* "fucntion" 17 times
* "functionn" 6 times
* "fuction" 6 times
* "fuunction" 4 times
* "functioin" 3 times
* "fonction" 3 times
* "funstion" twice
* "fnuction" once
* "functiom" once
* "functio" once
* "funcition" once
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22885 -
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Modified
Fri Mar 28 13:57:25 2008 UTC (6 years, 9 months ago) by
rdm
File length: 41390 byte(s)
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previous 20882
move the following directories under the new "math" meta directory:
mathcore
mathmore
fftw
foam
fumili
genvector
matrix
minuit
minuit2
mlp
physics
smatrix
splot
unuran
quadp
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10258 -
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Added
Fri Oct 8 09:07:10 2004 UTC (10 years, 3 months ago) by
brun
Original Path:
trunk/physics/src/TRobustEstimator.cxx
File length: 36958 byte(s)
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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