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Linear models have found widespread use in statistical investigations. Forevery linear model there exists a matrix representation for which the ReML(Restricted Maximum Likelihood) can be constructed from the elements of thecorresponding matrix. This method works in the standard manner when thecovariance structure is non-singular. It can also be used in the case where thecovariance structure is singular, because the method identifies particularnon-stochastic linear combinations of the observations which must beconstrained to zero. In order to use this method, the Cholesky decompositionhas to be generalized to symmetric and indefinite matrices using complexarithmetic methods. This method is applied to the problem of determining thespatial size (vertex) for the Higgs Boson decay in the Higgs -> 4 leptonchannel. A comparison based on the Chi-Square variable from the vertex fit forHiggs signal and t-tbar background is presented and shows that the backgroundcan be greatly suppressed using the Chi-Square variable. One of the majoradvantages of this novel method over the currently adopted technique ofb-tagging is that it is not affected by multiple interactions (pile up).

Automatic Methods for Handling Nearly Singular Covariance Structures Using the Cholesky Decomposition of an Indefinite Matrix