Entropy convergence of finite moment approximations in Hamburger and Stieltjes problems

被引：8

作者：

Milev, Mariyan ^{[1
]}

Tagliani, Aldo ^{[2
]}

机构：

[1] Univ Food Technol, Dept Informat & Stat, Plovdiv 4002, Bulgaria

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

来源：

STATISTICS & PROBABILITY LETTERS | 2017年 / 120卷

关键词：

Density; Moments; Maximum entropy; Entropy convergence; Hankel matrix; Hamburger and Stieltjes moment problem;

D O I：

10.1016/j.spl.2016.09.017

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：

The Hamburger and Stieltjes moment problem and the sequence of maximum entropy (MaxEnt) approximates with given moments are considered. MaxEnt approximate converges in entropy to the unknown distribution when the Hamburger (or Stieltjes) moment problem is determinate and the underlying distribution has finite entropy. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：114 / 117

页数：4

共 50 条

[41] NECESSARY AND SUFFICIENT CONDITIONS OF THE CONVERGENCE OF FINITE-DIMENSIONAL APPROXIMATIONS OF REGULARIZED PROBLEMS
TANANA, VP
DANILIN, AR
DOKLADY AKADEMII NAUK SSSR, 1982, 264 (05): : 1094 - 1096
[42] CONVERGENCE OF SOR ITERATIONS FOR FINITE ELEMENT APPROXIMATIONS TO ELLIPTIC BOUNDARY VALUE PROBLEMS
FIX, GJ
LARSEN, K
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1971, 8 (03) : 536 - &
[43] The Stieltjes condition and multidimensional K-moment problems
Schmuedgen, Konrad
ARCHIV DER MATHEMATIK, 2021, 117 (02) : 179 - 188
[44] On Convergence of Polynomial Approximations to the Gaussian Mixture Entropy
Dahlke, Caleb
Pacheco, Jason
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 36 (NEURIPS 2023), 2023,
[45] Relative entropy and moment problems
Georgiou, Tryphon T.
2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE, VOLS 1-8, 2005, : 4397 - 4403
[46] Finite moment problems: Geometry of the data space and conditioned maximum entropy solutions
Inglese, G.
Journal of Inverse and Ill-Posed Problems, 1995, 3 (03):
[47] Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems
Andreev, AB
Lazarov, RD
Racheva, MR
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 182 (02) : 333 - 349
[48] The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems
Rodriguez, R
Solomin, JE
MATHEMATICS OF COMPUTATION, 1996, 65 (216) : 1463 - 1475
[49] L-INFINITY-CONVERGENCE OF FINITE-ELEMENT GALERKIN APPROXIMATIONS FOR PARABOLIC PROBLEMS
NITSCHE, JA
RAIRO-ANALYSE NUMERIQUE-NUMERICAL ANALYSIS, 1979, 13 (01): : 31 - 54
[50] Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems
Hongtao Chen
Shanghui Jia
Hehu Xie
Applications of Mathematics, 2009, 54 : 237 - 250

← 1 2 3 4 5 →