Department of Mathematics
In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the prior information on the population covariance matrix. Analytical results on the improvement of the proposed shrinkage estimator are provided and some corresponding asymptotic properties are also derived. Finally, we demonstrate the practical improvement of the proposed method over existing methods through extensive simulation studies and real data analysis.
High-dimensional data, Large p small n, Shrinkage estimator, U-statistic
Source Publication Title
Journal of Multivariate Analysis
Copyright © 2014 Elsevier Inc. All rights reserved.
Cheng Wang’s research was supported by NSF of China Grants (No. 11101397, 71001095 and 11271347). Tiejun Tong’s research was supported by Hong Kong Research Grant HKBU202711 and Hong Kong Baptist University FRG Grands FRG2/10-11/020 and FRG2/11-12/110. Longbing Cao’s research was supported by Australian Research Council Discovery Grant DP1096218 and Australian Research Council Linkage Grant LP100200774.
Link to Publisher's Edition
Wang, C., Tong, T., Cao, L., & Miao, B. (2014). Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices. Journal of Multivariate Analysis, 125, 222-232. https://doi.org/10.1016/j.jmva.2013.12.012