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On shrinkage estimation for balanced loss functions

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  • Marchand, Éric
  • Strawderman, William E.

Abstract

The estimation of a multivariate mean θ is considered under natural modifications of balanced loss functions of the form: (i) ωρ(‖δ−δ0‖2)+(1−ω)ρ(‖δ−θ‖2), and (ii) ℓω‖δ−δ0‖2+(1−ω)‖δ−θ‖2, where δ0 is a target estimator of γ(θ). After briefly reviewing known results for original balanced loss with identity ρ or ℓ, we provide, for increasing and concave ρ and ℓ which also satisfy a completely monotone property, Baranchik-type estimators of θ which dominate the benchmark δ0(X)=X for X either distributed as multivariate normal or as a scale mixture of normals. Implications are given with respect to model robustness and simultaneous dominance with respect to either ρ or ℓ.

Suggested Citation

  • Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:jmvana:v:175:y:2020:i:c:s0047259x19301770
    DOI: 10.1016/j.jmva.2019.104558
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    References listed on IDEAS

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    1. Jafari Jozani, Mohammad & Marchand, Éric & Parsian, Ahmad, 2006. "On estimation with weighted balanced-type loss function," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 773-780, April.
    2. Qiang Zhang & Ping Chen, 2018. "Credibility estimators with dependence structure over risks and time under balanced loss function," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(2), pages 157-173, May.
    3. Hu, Guikai & Peng, Ping, 2011. "All admissible linear estimators of a regression coefficient under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1217-1224, September.
    4. Dey, Dipak K. & Ghosh, Malay & Strawderman, William E., 1999. "On estimation with balanced loss functions," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 97-101, November.
    5. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On improved shrinkage estimators for concave loss," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 241-246.
    6. Ann Brandwein & Stefan Ralescu & William Strawderman, 1993. "Shrinkage estimators of the location parameter for certain spherically symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 551-565, September.
    7. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
    8. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    9. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2014. "Bayes minimax estimation of the multivariate normal mean vector under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 96-101.
    10. Jerzy Baran & Agnieszka Stępień-Baran, 2013. "Sequential estimation of a location parameter and powers of a scale parameter from delayed observations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(3), pages 263-280, August.
    11. Strawderman, William E., 1974. "Minimax estimation of location parameters for certain spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 255-264, September.
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    Cited by:

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