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Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1173–1188 | Cite as

A new estimator of covariance matrix via partial Iwasawa coordinates

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Abstract

This paper is concerned with the problem of improving the estimator of covariance matrix under Stein’s loss. By the partial Iwasawa coordinates of covariance matrix, the corresponding risk can be split into three parts. One can use the information in the weighted matrix of weighted quadratic loss to improve one part of risk. However, this paper indirectly takes advantage of the information in the sample mean and reuses Iwasawa coordinates to improve the rest of risk. It is worth mentioning that the process above can be repeated. Finally, a Monte Carlo simulation study is carried out to verify the theoretical results.

Keywords

Covariance matrix James–Stein estimator partial Iwasawa coordinates Stein’s loss weighted quadratic loss 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Statistics and ManagementShanghai University of Finance and EconomicsShanghaiChina

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