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Computing Projections into Cones Generated by a Matrix
Author(s) -
Frick H.
Publication year - 1997
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710390808
Subject(s) - mathematics , estimator , simple (philosophy) , function (biology) , maximization , expectation–maximization algorithm , maxima , matrix (chemical analysis) , maximum likelihood , mathematical optimization , m estimator , algorithm , combinatorics , statistics , art , philosophy , materials science , epistemology , evolutionary biology , performance art , composite material , biology , art history
A method is described for computing orthogonal projections into finitely generated cones. This method can be used to solve nonnegative least squares approximation problems, to find the multivariate onesided Maximum Likelihood estimator and also determines the most stringent somewhere most powerful test of Schaafsma. The gist of the procedure is the unconstrained maximization of a numerically simple function. This function has a global maximum and allows an uncomplicated maximum search since local maxima do not exist. The maximum can be obtained after a finite number of iterations.