非正态多元线性模型中的二阶偏差校正的Akaike信息准则

发布时间：2018-07-07 14:15

本文选题：Akaike信息准则 + Kullback-Leibler信息　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：本文主要论述了一种新型的信息准则,偏置校正的Akaike信息准则(AIC)。当数据的真实分布是正态分布时,有很多的信息准则在对这样的数据做变量选择都有很好的效果,但如果数据的真实分布为非正态分布时,往往没有一个特别好的方法来进行变量选择。本文介绍的一种偏置校正的Akaike信息准则,这种信息准则解决了当所观察的数据的真实分布是一种未知的非正态分布时,它可以为多元正态线性回归模型提供一种效果较好的变量选择的方法。众所周知的是,当数据的真实分布为非正态分布时,使用AIC准则来进行变量选择时,产生的偏差是O(1),此外还有一些一阶偏差校正的信息准则方法,它们可以将这种偏差降低到O(n-1),其中n表示样本大小。本文提出了一种新的信息准则,这种信息准则在一阶偏差校正的AIC准则的基础上稍微做了一些调整。虽然这种调整仅仅通过调整常数系数,但是这种新标准的偏差降低到O(n-2)。与此同时,新的准则产生的方差也有所降低。最后通过数值实验,我们验证了我们的新的信息准则标准是优于之前的方法的。
[Abstract]:In this paper, a new information criterion, bias corrected Akaike information criterion (AICs), is presented. When the true distribution of data is normal, there are many information criteria which have good effect on the variable selection of such data, but if the true distribution of data is non-normal distribution, There is often no particularly good way to select variables. This paper introduces a bias corrected Akaike information criterion, which solves the problem when the true distribution of observed data is an unknown non-normal distribution. It can provide a better method of variable selection for multivariate normal linear regression model. It is well known that when the true distribution of data is non-normal, the deviation is O (1) when the AIC criterion is used to select variables. In addition, there are some information criterion methods for first-order deviation correction. They can reduce the deviation to O (n-1), where n represents the sample size. In this paper, a new information criterion is proposed, which is based on the first order deviation correction AIC criterion. Although the adjustment is only by adjusting the constant coefficient, the deviation of the new standard is reduced to O (n-2). At the same time, the variance of the new criterion is also reduced. Finally, through numerical experiments, we verify that our new information criterion is superior to the previous method.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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