Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices

Cheng Wang, Tiejun TONG*, Longbing Cao, Baiqi Miao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)222-232
Number of pages11
JournalJournal of Multivariate Analysis
Volume125
DOIs
Publication statusPublished - Mar 2014

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • High-dimensional data
  • Large p small n
  • Shrinkage estimator
  • U-statistic

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