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
收藏
页码：3596 / 3601
页数：6
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