CONSISTENCY OF AIC AND BIC IN ESTIMATING THE NUMBER OF SIGNIFICANT COMPONENTS IN HIGH-DIMENSIONAL PRINCIPAL COMPONENT ANALYSIS
CONSISTENCY OF AIC AND BIC IN ESTIMATING THE NUMBER OF SIGNIFICANT COMPONENTS IN HIGH-DIMENSIONAL PRINCIPAL COMPONENT ANALYSIS
复制标题
高维主成分分析中AIC和BIC估计显着成分数的一致性
DOI：
10.1214/17-aos1577
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发表时间：
2018-06-01
影响因子：
4.5
通讯作者：
Fujikoshi, Yasunori
中科院分区：
文献类型：
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作者：
Bai, Zhidong;Choi, Kwok Pui;Fujikoshi, Yasunori
本文研究了主成分分析中显著成分个数的估计问题，它对应于p个变量的协方差矩阵的主特征值个数。我们的目的是检查的一致性的估计标准AIC和BIC的基础上的模型选择标准赤池[在第二届国际信息理论研讨会（1973年）267-281，Akademia Kiado]和施瓦茨[估计模型的维数6（1978年）461464]下的高维渐近框架。使用随机矩阵理论的技术，我们得到的条件是强一致的情况下，当占主导地位的人口特征值是有界的，当占主导地位的特征值趋于无穷大的准则。在不对总体分布作正态性假设的情况下，得到了渐近结果。仿真研究表明，我们的定理中的充分条件是必要的。
In this paper, we study the problem of estimating the number of significant components in principal component analysis (PCA), which corresponds to the number of dominant eigenvalues of the covariance matrix of p variables. Our purpose is to examine the consistency of the estimation criteria AIC and BIC based on the model selection criteria by Akaike [In 2nd International Symposium on Information Theory (1973) 267-281, Akademia Kiado] and Schwarz [Estimating the dimension of a model 6 (1978) 461464] under a high-dimensional asymptotic framework. Using random matrix theory techniques, we derive sufficient conditions for the criterion to be strongly consistent for the case when the dominant population eigenvalues are bounded, and when the dominant eigenvalues tend to infinity. Moreover, the asymptotic results are obtained without normality assumption on the population distribution. Simulation studies are also conducted, and results show that the sufficient conditions in our theorems are essential.