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James–Stein type estimators of variances

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  • Tong, Tiejun
  • Jang, Homin
  • Wang, Yuedong

Abstract

In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic properties are investigated under two schemes when either the number of degrees of freedom of each individual estimate or the number of individuals approaches to infinity. Simulation studies indicate that the performance of various shrinkage estimators depends on the loss function, and the proposed estimator outperforms existing methods under the squared loss function.

Suggested Citation

  • Tong, Tiejun & Jang, Homin & Wang, Yuedong, 2012. "James–Stein type estimators of variances," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 232-243.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:232-243
    DOI: 10.1016/j.jmva.2012.01.019
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    References listed on IDEAS

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    1. Tong, Tiejun & Wang, Yuedong, 2007. "Optimal Shrinkage Estimation of Variances With Applications to Microarray Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 113-122, March.
    2. Herbert Pang & Tiejun Tong & Hongyu Zhao, 2009. "Shrinkage-based Diagonal Discriminant Analysis and Its Applications in High-Dimensional Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1021-1029, December.
    3. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
    4. Opgen-Rhein Rainer & Strimmer Korbinian, 2007. "Accurate Ranking of Differentially Expressed Genes by a Distribution-Free Shrinkage Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-20, February.
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    Cited by:

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