Regularization for high-dimensional covariance matrix

@article{XiangzhaoCui2016,
abstract = {In many applications, high-dimensional problem may occur often for various reasons, for example, when the number of variables under consideration is much bigger than the sample size, i.e., p >> n. For highdimensional data, the underlying structures of certain covariance matrix estimates are usually blurred due to substantial random noises, which is an obstacle to draw statistical inferences. In this paper, we propose a method to identify the underlying covariance structure by regularizing a given/estimated covariance matrix so that the noises can be filtered. By choosing an optimal structure from a class of candidate structures for the covariance matrix, the regularization is made in terms of minimizing Frobenius-norm discrepancy. The candidate class considered here includes the structures of order-1 moving average, compound symmetry, order-1 autoregressive and order-1 autoregressive moving average. Very intensive simulation studies are conducted to assess the performance of the proposed regularization method for very high-dimensional covariance problem. The simulation studies also show that the sample covariance matrix, although performs very badly in covariance estimation for high-dimensional data, can be used to correctly identify the underlying structure of the covariance matrix. The approach is also applied to real data analysis, which shows that the proposed regularization method works well in practice.},
author = {Xiangzhao Cui, Chun Li, Jine Zhao, Li Zeng, Defei Zhang, Jianxin Pan},
journal = {Special Matrices},
keywords = {High-dimensional; Covariance estimation; Covariance structure; Regularization; high-dimensional; covariance estimation; covariance structure; regularization},
language = {eng},
number = {1},
pages = {189-201},
title = {Regularization for high-dimensional covariance matrix},
url = {http://eudml.org/doc/277091},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Xiangzhao Cui
AU - Chun Li
AU - Jine Zhao
AU - Li Zeng
AU - Defei Zhang
AU - Jianxin Pan
TI - Regularization for high-dimensional covariance matrix
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 189
EP - 201
AB - In many applications, high-dimensional problem may occur often for various reasons, for example, when the number of variables under consideration is much bigger than the sample size, i.e., p >> n. For highdimensional data, the underlying structures of certain covariance matrix estimates are usually blurred due to substantial random noises, which is an obstacle to draw statistical inferences. In this paper, we propose a method to identify the underlying covariance structure by regularizing a given/estimated covariance matrix so that the noises can be filtered. By choosing an optimal structure from a class of candidate structures for the covariance matrix, the regularization is made in terms of minimizing Frobenius-norm discrepancy. The candidate class considered here includes the structures of order-1 moving average, compound symmetry, order-1 autoregressive and order-1 autoregressive moving average. Very intensive simulation studies are conducted to assess the performance of the proposed regularization method for very high-dimensional covariance problem. The simulation studies also show that the sample covariance matrix, although performs very badly in covariance estimation for high-dimensional data, can be used to correctly identify the underlying structure of the covariance matrix. The approach is also applied to real data analysis, which shows that the proposed regularization method works well in practice.
LA - eng
KW - High-dimensional; Covariance estimation; Covariance structure; Regularization; high-dimensional; covariance estimation; covariance structure; regularization
UR - http://eudml.org/doc/277091
ER -