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The support reduction algorithm for computing non-parametric function estimates in mixture models. (English) Zbl 1199.65017

A new iterative algorithm (called support reduction, SR-algorithm) is described for minimization of convex functionals from bounded discrete positive measures with finite support. During each iteration, the algorithm adds one new support point to the existing iterate. After that, as many support points of the measure as possible are deleted resulting in a sparse next iterate. This algorithm is applied to the least squares estimation of convex regression function, to maximum likelihood deconvolution and to the statistical analysis of quantum non-locality experiments. The algorithm is compared to the EM-algorithm and the interior point algorithm.

MSC:

65C60 Computational problems in statistics (MSC2010)
62G08 Nonparametric regression and quantile regression
62J02 General nonlinear regression

Software:

MLEcens
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References:

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