Fractional Moments and Maximum Entropy: Geometric Meaning

被引：4

作者：

Gzyl, Henryk ^{[1
]}

Inverardi, Pier Luigi Novi ^{[2
]}

Tagliani, Aldo ^{[2
]}

机构：

[1] Ctr Finanzas IESA, DF, Caracas, Venezuela

[2] Univ Trento, Dept Econ & Management, I-38100 Trento, Trento, Italy

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2014年 / 43卷 / 17期

关键词：

Fractional moments; Hermite-Birkoff interpolation; Kullback Leibler distance; Maximum entropy;

D O I：

10.1080/03610926.2012.705212

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the problem of recovering a probability density on a bounded or unbounded subset D of [0, infinity), 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.

引用

页码：3596 / 3601

页数：6

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