Fractional Moments and Maximum Entropy: Geometric Meaning |
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| Authors: | Henryk Gzyl Pier Luigi Novi Inverardi |
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| Institution: | 1. Centro de Finanzas IESA, DF, Caracas, Venezuela;2. Department of Economics and Management, University of Trento, Trento, Italy |
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| Abstract: | We consider the problem of recovering a probability density on a bounded or unbounded subset D of 0, ∞), from the knowledge of its sequence of fractional moments within a maximum entropy (MaxEnt) setup. Based upon entropy convergence results previously formulated, the fractional moments are selected so that the entropy of the MaxEnt approximation be minimum. A geometric interpretation of the reconstruction procedure is formulated as follows: the two moment curves generated by the unknown density and its MaxEnt approximation are interpolating in Hermite-Birkoff sense; that is, they are both interpolating and tangent at the selected nodes. |
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| Keywords: | Fractional moments Hermite-Birkoff interpolation Kullback Leibler distance Maximum entropy |
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