把Sibson的Lemme 2.1推廣成二階的擾動.因此我們可以得到特徵值和特徵向量的二階影響函數,進而我們可以用來檢測那些互相遮蓋的影響點.此外,在穩健性的討論中,我們給予那些有影響的點較小的權重.最後我們利用一個實例來說明以上介紹的方法. Lemma 2.1 of Sibson (1979) is generalized to the second order perturbation of a symmetric matrix. Thus, the second order theoretical influence functions for the eigenvalues and eigenvectors can be developed to detect the masked influential observations in principal component analysis. In addition, a robust principal component can thus be developed by downweighting the identified influential observations. Numerical example illustrates the techniques.
