A0816
Title: Estimation of the strongly spiked eigenstructure in high-dimensional settings
Authors: Kazuyoshi Yata - University of Tsukuba (Japan) [presenting]
Aki Ishii - Tokyo University of Science (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: High-dimensional data often have a low-rank structure which contains strongly spiked eigenvalues. The problem of estimating the strongly spiked eigenstructure in high-dimensional situations is considered. First, the conventional PCA is considered to estimate the structure, showing that the estimation holds consistency properties under severe conditions. The conventional PCA is heavily subjected to noise. Recently, consistent estimators of the strongly spiked eigenvalues and eigenvectors have been given by developing a new PCA method called the Automatic Sparse PCA (A-SPCA) methodology. To remove the noise, the A-SPCA is applied and propose a new estimation of the strongly spiked eigenstructure. The proposed estimation by the A-SPCA holds the consistency properties under mild conditions and effectively improves the conventional PCA's error rate effectively. Finally, the performance of the proposed estimation is investigated in actual data analyses.
