High-dimensional correlation matrix estimation for general continuous data with Bagging technique

Abstract

High-dimensional covariance matrix estimation plays a central role in multivariate statistical analysis. It is well-known that the sample covariance matrix is singular when the sample size is smaller than the dimension of the variable, but the covariance estimate must be positive-definite. This motivates some modifications of the sample covariance matrix to preserve its efficient estimation of pairwise covariance. In this paper, we modify the sample correlation matrix using the Bagging technique. The proposed Bagging estimator is flexible for general continuous data. Under some mild conditions, we show theoretically that the Bagging estimator can ensure positive-definiteness with probability one in finite samples. We also prove the consistency of the bootstrap estimator of Pearson correlation and the consistency of our Bagging estimator when the dimension p is fixed. Simulation results and a real application are provided to demonstrate that our method strikes a better balance between RMSE and likelihood, and is more robust, than other existing estimators.