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信息复杂性准则的深入探讨

吕纯濂   

  1. 南京信息工程大学数理学院, 南京 210044
  • 收稿日期:2005-01-26 修回日期:2008-01-21 出版日期:2008-06-25 发布日期:2008-06-25

吕纯濂. 信息复杂性准则的深入探讨[J]. 系统科学与数学, 2008, 28(6): 758-768.

LV Chunlian. On Informational Complexity Criteria[J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(6): 758-768.

On Informational Complexity Criteria

LV Chunlian   

  1. College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2005-01-26 Revised:2008-01-21 Online:2008-06-25 Published:2008-06-25
介绍联系拟合优度与模型复杂性测度的一种模型选择准则─信息复杂性ICOMP)准则的基本原理. 由Bozdogan提出的信息复杂性(ICOMP)准则可以视为两个Kullback-Leibler距离之和的一种近似. 首先研究了所考虑模型中有真实模型的情况下, ICOMP准则类的渐近相容性;然后又介绍并完成了所考虑模型中没有真实模型的情况下, ICOMP准则类的渐近相容性. 在有限样本容量的情况下,用ICOMP 准则选择的估计模型,比用其他通用的准则选择的估计模型,更接近于真实模型.
A rationale for model selection criteria ─ Informational Complexity (ICOMP) Criteria, that combine a badness-of-fit term with a measure of complexity of a model, is introduced. The ICOMP criterion suggested by Bozdogan is seen as an approximation to the sum of two Kullback-Leibler distances. The asymptotic consistency properties of the class of ICOMP criteria are investigated first in the case when one of the models considered is the true model, and then in the case when none of the models is the true model. With finite sample size, the model selected by ICOMP is closer to the true model than the ones obtained by existing methods.

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