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On estimation with balanced loss functions

Author

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  • Dey, Dipak K.
  • Ghosh, Malay
  • Strawderman, William E.

Abstract

Zellner ((1994) in: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390), introduced the notion of a balanced loss function in the context of a general linear model to reflect both goodness of fit and precision of estimation. We study this notion from the perspective of unifying a variety of results both frequentist and Bayesian. We show in broad generality that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for normal error structures and more generally for spherically symmetric error distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:2:p:97-101
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    References listed on IDEAS

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    1. 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.
    2. Cellier, D. & Fourdrinier, D., 1995. "Shrinkage Estimators under Spherical Symmetry for the General Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 338-351, February.
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    Cited by:

    1. Gómez-Déniz, E., 2008. "A generalization of the credibility theory obtained by using the weighted balanced loss function," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 850-854, April.
    2. Cao, Ming-Xiang & He, Dao-Jiang, 2017. "Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 246-254.
    3. N. Farsipour & A. Asgharzadeh, 2004. "Estimation of a normal mean relative to balanced loss functions," Statistical Papers, Springer, vol. 45(2), pages 279-286, April.
    4. A. Asgharzadeh & N. Sanjari Farsipour, 2008. "Estimation of the exponential mean time to failure under a weighted balanced loss function," Statistical Papers, Springer, vol. 49(1), pages 121-131, March.
    5. 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.
    6. Chaturvedi, Anoop & Shalabh, 2004. "Risk and Pitman closeness properties of feasible generalized double k-class estimators in linear regression models with non-spherical disturbances under balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 229-256, August.
    7. van Akkeren, Marco & Judge, George & Mittelhammer, Ron, 2002. "Generalized moment based estimation and inference," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 127-148, March.
    8. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    9. 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.
    10. Cao, Mingxiang, 2014. "Admissibility of linear estimators for the stochastic regression coefficient in a general Gauss–Markoff model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 25-30.
    11. 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.
    12. 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.
    13. Hobbad, Lahoucine & Marchand, Éric & Ouassou, Idir, 2021. "On shrinkage estimation of a spherically symmetric distribution for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    14. Zellner, Arnold, 2010. "Bayesian shrinkage estimates and forecasts of individual and total or aggregate outcomes," Economic Modelling, Elsevier, vol. 27(6), pages 1392-1397, November.

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