期刊文献+

An Alternating Iterative Method and Its Application in Statistical Inference 被引量:4

An Alternating Iterative Method and Its Application in Statistical Inference
原文传递
导出
摘要 This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. (Biometrika, 72, 465472 (1983)), Shi N. Z. (J. Multivariate Anal., 50, 282-293 (1994)) and El Barmi H. and Dykstra R. (Ann. Statist., 26, 1878 1893 (1998)). This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. (Biometrika, 72, 465472 (1983)), Shi N. Z. (J. Multivariate Anal., 50, 282-293 (1994)) and El Barmi H. and Dykstra R. (Ann. Statist., 26, 1878 1893 (1998)).
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第5期843-856,共14页 数学学报(英文版)
基金 the National Natural Science Foundation of China (Nos.10431010,10501005) Science Foundation for Young Teachers of NENU (No.20070103)
关键词 semi-convex function alternating iterative method accumulation point maximum likelihood estimation order restriction semi-convex function, alternating iterative method, accumulation point, maximum likelihood estimation, order restriction
  • 相关文献

参考文献1

二级参考文献9

  • 1史宁中,Appl Statist,1992年
  • 2Liu W,Northeast Math,1992年
  • 3Geng Z,Appl Statist,1991年,40卷
  • 4史宁中,Chin Ann Math B,1991年
  • 5史宁中,J Am Statist Assoc,1991年,86卷,154页
  • 6Geng Z,J Jpn Soc Comp,1991年,4卷,49页
  • 7Geng Z,Appl Statist,1990年,39卷,397页
  • 8史宁中,Commun Statist,1988年,17卷,657页
  • 9史宁中,Memoir Faculty Sci Kyuzhu Univ,1988年,42卷,109页

共引文献32

同被引文献1

引证文献4

二级引证文献3

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部