A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large
A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large
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DOI：
10.1214/15-ejs1022
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发表时间：
2015
影响因子：
1.1
通讯作者：
H. Yanagihara;H. Wakaki;Y. Fujikoshi
中科院分区：
文献类型：
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作者：
H. Yanagihara;H. Wakaki;Y. Fujikoshi
众所周知，赤池信息准则（AIC）不是一个一致的模型选择准则。这种不一致性已被证实从一个大样本渐近框架评估的渐近选择概率。然而，当一个高维的渐近框架，使响应变量的维数和样本容量接近1，用于评估选择概率，我们可以证明的一致性性质的AIC选择变量的多元线性模型。这意味着当样本量和维度同时接近1时，AIC选择真实模型的概率为1。的一致性属性也检查数值进行Monte Carlo模拟。
It is common knowledge that the Akaike’s information criterion (AIC) is not a consistent model selection criterion. This inconsistency property has been confirmed from an asymptotic selection probability evaluated from a large-sample asymptotic framework. However, when a high-dimensional asymptotic framework, such that the dimension of the response variables and the sample size are approaching 1, is used for evaluating the selection probability, we can prove a consistency property of the AIC for selecting variables in multivariate linear models. This means that the probability of selecting the true model by the AIC goes to 1 as the sample size and the dimension simultaneously approach 1. The consistency property is also checked numerically by conducting a Monte Carlo simulation.