On the number of principal components in high dimensions
针对维度远高于样本量的高维数据，提出通过检验残差得分平方长度的偏度来顺序确定主成分个数的方法，并在模拟和实例中表现良好。
We consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is shown to be consistent, performs well in high-dimensional simulation studies, and provides reasonable estimates in examples.