论文标题
高维PCA等级选择的广义信息标准
A generalized information criterion for high-dimensional PCA rank selection
论文作者
论文摘要
主成分分析（PCA）是降低维度最常用的统计程序。应用PCA的一个重要问题是确定等级，这是协方差矩阵的主要特征值的数量。 Akaike信息标准（AIC）和贝叶斯信息标准（BIC）是使用最广泛的等级选择方法之一。两者都使用免费参数的数量来评估模型复杂性。在这项工作中，我们采用广义信息标准（GIC）在高维框架下为PCA排名选择了一种新方法。 GIC模型的复杂性考虑了协方差特征值的大小，并且可以更好地适应实际应用。得出了GIC的渐近特性，并在广义的尖峰协方差模型下建立了选择一致性。
Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) are among the most widely used rank selection methods. Both use the number of free parameters for assessing model complexity. In this work, we adopt the generalized information criterion (GIC) to propose a new method for PCA rank selection under the high-dimensional framework. The GIC model complexity takes into account the sizes of covariance eigenvalues and can be better adaptive to practical applications. Asymptotic properties of GIC are derived and the selection consistency is established under the generalized spiked covariance model.
