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Mathematical Problems in Engineering Volume 2019 ,2019-01-16
Some Notes on Concordance between Optimization and Statistics
Research Article
Weiyan Mu 1 Qiuyue Wei 1 Shifeng Xiong 2
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DOI:10.1155/2019/3485064
Received 2018-10-25, accepted for publication 2018-12-17, Published 2018-12-17
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摘要

Many engineering problems require solutions to statistical optimization problems. When the global solution is hard to attain, engineers or statisticians always use the better solution because we intuitively believe a principle, called better solution principle (BSP) in this paper, that a better solution to a statistical optimization problem also has better statistical properties of interest. This principle displays some concordance between optimization and statistics and is expected to widely hold. Since theoretical study on BSP seems to be neglected by statisticians, this paper presents a primary discussion on BSP within a relatively general framework. We demonstrate two comparison theorems as the key results of this paper. Their applications to maximum likelihood estimation are presented. It can be seen that BSP for this problem holds under reasonable conditions; i.e., an estimator with greater likelihood is better in some statistical sense.

授权许可

Copyright © 2019 Weiyan Mu et al. 2019
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

通讯作者

Shifeng Xiong.NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, cas.cn.xiong@amss.ac.cn

推荐引用方式

Weiyan Mu,Qiuyue Wei,Shifeng Xiong. Some Notes on Concordance between Optimization and Statistics. Mathematical Problems in Engineering ,Vol.2019(2019)

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