A0462
Title: Sparse estimation of cross-covariance matrices in high-dimension, low-sample-size settings
Authors: Kazuyoshi Yata - University of Tsukuba (Japan) [presenting]
Tetsuya Umino - University of Tsukuba (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: Sparse estimation of the entire covariance matrix has been studied extensively. However, research focused on estimating the cross-covariance matrix in high-dimensional settings is limited. A novel thresholding estimator of the cross-covariance matrix is proposed for high-dimension, low-sample-size (HDLSS) settings. The asymptotic properties of the sample cross-covariance matrix are first investigated, and it is shown that the estimator contains large amounts of noise in HDLSS setting, which renders it inconsistent. Sparse principal component analysis (SPCA) methods have been investigated for the sparse estimation of principal component directions. A recent study proposed a new SPCA called the automatic SPCA (A-SPCA). A-SPCA determines its threshold automatically and has been shown to be consistent under mild conditions. The purpose is to extend the A-SPCA methodology to the estimation of high-dimensional cross-covariance matrices and propose a new sparse estimator based on this approach. It is shown that the proposed estimator is consistent under mild conditions in HDLSS settings. Its performance is evaluated through empirical analysis using gene expression data.
