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Expansions for the risk of Stein type estimates for non-normal data

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  • Withers Christopher S.

    (Applied Mathematics Group, Industrial Research Limited, Neuseeland)

  • Nadarajah Saralees

Abstract

We consider the James–Stein problem for non-normal data for estimating a p-vector θ. It is shown how the risk may be expanded in powers of p-1. The factor 1-2/p that distinguishes the James–Stein estimate from the Stein estimate is shown to have only O(p-2) effect on the risk. The case, where the variance must be estimated is studied for the one-way unbalanced ANOVA problem.

Suggested Citation

  • Withers Christopher S. & Nadarajah Saralees, 2011. "Expansions for the risk of Stein type estimates for non-normal data," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 81-95, May.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:2:p:81-95:n:1
    DOI: 10.1524/stnd.2011.1054
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    References listed on IDEAS

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    1. Yeung Lewis Chan & James H. Stock & Mark W. Watson, 1999. "A dynamic factor model framework for forecast combination," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 91-121.
    2. Helge Blaker, 1999. "Shrinkage and Orthogonal Decomposition," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 1-15, March.
    3. C. Withers, 1991. "A class of multiple shrinkage estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 147-156, March.
    4. Nicoleta Serban, 2008. "Estimating and clustering curves in the presence of heteroscedastic errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 553-571.
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    Cited by:

    1. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.

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