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On SURE-Type Double Shrinkage Estimation

Author

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  • Bing-Yi Jing
  • Zhouping Li
  • Guangming Pan
  • Wang Zhou

Abstract

The article is concerned with empirical Bayes shrinkage estimators for the heteroscedastic hierarchical normal model using Stein's unbiased estimate of risk (SURE). Recently, Xie, Kou, and Brown proposed a class of estimators for this type of problems and established their asymptotic optimality properties under the assumption of known but unequal variances. In this article, we consider this problem with unequal and unknown variances, which may be more appropriate in real situations. By placing priors for both means and variances, we propose novel SURE-type double shrinkage estimators that shrink both means and variances. Optimal properties for these estimators are derived under certain regularity conditions. Extensive simulation studies are conducted to compare the newly developed methods with other shrinkage techniques. Finally, the methods are applied to the well-known baseball dataset and a gene expression dataset. Supplementary materials for this article are available online.

Suggested Citation

  • Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:516:p:1696-1704
    DOI: 10.1080/01621459.2015.1110032
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    References listed on IDEAS

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    2. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
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    4. 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.
    5. J. T. Gene Hwang & Jing Qiu & Zhigen Zhao, 2009. "Empirical Bayes confidence intervals shrinking both means and variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 265-285, January.
    6. Xianchao Xie & S. C. Kou & Lawrence D. Brown, 2012. "SURE Estimates for a Heteroscedastic Hierarchical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1465-1479, December.
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    Cited by:

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    2. Sinha, Shyamalendu & Hart, Jeffrey D., 2019. "Estimating the mean and variance of a high-dimensional normal distribution using a mixture prior," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 201-221.
    3. Chen, Yongzhao & Cheung, Ka Chun & Choi, Hugo Ming Cheung & Yam, Sheung Chi Phillip, 2020. "Evolutionary credibility risk premium," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 216-229.

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