A0703
Title: Estimation of eigenvectors for linear combinations of high-dimensional covariance matrices and its application
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 non-sparse and low-rank structure which contains strongly spiked eigenvalues. We call it the strongly spiked eigenvalue (SSE) model. We note that, under the SSE model, asymptotic normality is not valid because it is heavily influenced by strongly spiked eigenvalues. Recently, consistent estimators of eigenvectors for each high-dimensional covariance matrix have been given by developing a new PCA method called the noise-reduction (NR) methodology. A data transformation technique that transforms the SSE model into the non-SSE model has also been provided by using the NR method. Under the non-SSE model, we can ensure high accuracy for inferences by using the asymptotic normality. We consider the estimation of eigenvectors for linear combinations of the high-dimensional covariance matrices. We give a consistent estimator of the eigenvectors by developing the NR method. By using the estimator, we give a new data transformation technique that transforms the SSE model into the non-SSE model for the linear combinations. We propose a statistic for the linear combinations of mean vectors and prove that the statistic establishes the asymptotic normality. Finally, we investigate the performance of the statistic in actual data analyses.
