IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i8p773-780.html
   My bibliography  Save this article

On estimation with weighted balanced-type loss function

Author

Listed:
  • Jafari Jozani, Mohammad
  • Marchand, Éric
  • Parsian, Ahmad

Abstract

For estimating an unknown parameter [theta], we introduce and motivate the use of the balanced-type loss function: , where 0[less-than-or-equals, slant][omega][less-than-or-equals, slant]1, q([theta]) is a positive weight function, and [delta]0 is a general "target" estimator. Developments and various examples are given with regards to the issues of admissibility, dominance, Bayesianity, and minimaxity. In many cases, as in Dey et al. [1999. On estimation with balanced loss functions. Statist. Probab. Lett. 45, 97-101], we show that results for loss L[omega],[delta]0 may be inferred directly from corresponding results for weighted squared error loss (i.e., [omega]=0). Specific issues related to constrained parameter spaces, which include the choice of the target estimator, are addressed. Finally, we derive minimax estimators of a bounded normal mean [theta] under loss L[omega],[delta]0 with [delta]0 being the maximum-likelihood estimator of [theta].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:773-780
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00385-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chou Jine-phone, 1995. "Admissibility Of Conjugate Bayes Estimators For The Mean Of A Negative Binomial Distribution," Statistics & Risk Modeling, De Gruyter, vol. 13(4), pages 301-306, April.
    2. Dey Dipak K. & Kim Chansoo & Chung Younshik, 1999. "A New Class Of Minimax Estimators Of Multivariate Normal Mean Vectors Under Balanced Loss Function," Statistics & Risk Modeling, De Gruyter, vol. 17(3), pages 255-266, March.
    3. 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.
    4. Éric Marchand & William Strawderman, 2005. "Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 129-143, March.
    5. Chung Younshik & Kim Chansoo & Song Seongho, 1998. "Linear Estimators Of A Poisson Mean Under Balanced Loss Functions," Statistics & Risk Modeling, De Gruyter, vol. 16(3), pages 245-258, March.
    6. Jozani, Mohammad Jafari & Nematollahi, Nader & Shafie, Khalil, 2002. "An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 437-444, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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. Mehrjoo, Mehrdad & Jafari Jozani, Mohammad & Pawlak, Miroslaw, 2021. "Toward hybrid approaches for wind turbine power curve modeling with balanced loss functions and local weighting schemes," Energy, Elsevier, vol. 218(C).
    5. Jafar Ahmadi & Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2009. "Prediction of k-records from a general class of distributions under balanced type loss functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 19-33, June.
    6. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    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. Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    9. 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.
    10. 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).
    11. Stoltenberg, Emil Aas & Hjort, Nils Lid, 2020. "Multivariate estimation of Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    12. Hu, Guikai & Peng, Ping, 2012. "Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 286-295.
    13. Refah Alotaibi & Hoda Rezk & Sanku Dey & Hassan Okasha, 2021. "Bayesian estimation for Dagum distribution based on progressive type I interval censoring," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-17, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
    5. 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.
    6. Rufo, M.J. & Martín, J. & Pérez, C.J., 2016. "A Bayesian negotiation model for quality and price in a multi-consumer context," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 132-141.
    7. Hisayuki Tsukuma & Tatsuya Kubokawa, 2015. "Minimaxity in estimation of restricted and non-restricted scale parameter matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 261-285, April.
    8. 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.
    9. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On predictive density estimation for location families under integrated squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 57-74.
    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. Alicja Jokiel-Rokita, 2011. "Bayes sequential estimation for a particular exponential family of distributions under LINEX loss," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 211-219, September.
    12. 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.
    13. Tatsuya Kubokawa & William E. Strawderman, 2010. "Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems," CIRJE F-Series CIRJE-F-749, CIRJE, Faculty of Economics, University of Tokyo.
    14. 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).
    15. 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.
    16. 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.
    17. 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.
    18. Rufo, M.J. & Martín, J. & Pérez, C.J., 2014. "Adversarial life testing: A Bayesian negotiation model," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 118-125.
    19. Leila Golparver & Ali Karimnezhad & Ahmad Parsian, 2013. "Optimal rules and robust Bayes estimation of a Gamma scale parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 595-622, July.
    20. Tatsuya Kubokawa, 2010. "Minimax Estimation of Linear Combinations of Restricted Location Parameters," CIRJE F-Series CIRJE-F-723, CIRJE, Faculty of Economics, University of Tokyo.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:773-780. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.