Nonparametric maximum likelihood estimation of a probability density via mathematical programming |
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Authors: | Dr. J. Fischer |
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Affiliation: | (1) Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-7000 Stuttgart 80 |
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Abstract: | Based on sample values of a one-dimensional random variable a nonparametric maximum likelihood estimate for the unknown probability density is introduced as the solution of an optimization problem in an appropriate Hilbert space. This solution turns out to be a polynomial spline function, and a complete characterization is given using recent results on the differentiability of the optimal value of a parametrized family of optimization problems. An important feature of this estimate is that its support interval results in a quite natural way from the formulation of the problem and is not fixed in advance. The estimator is shown to have a certain consistency property for a special class of density functions. Numerical results will be given in a subsequent paper. |
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