IDEAS home Printed from https://ideas.repec.org/p/vic/vicewp/0004.html
   My bibliography  Save this paper

Preliminary-Test and Bayes Estimation of a Location Parameter Under 'Reflected Normal' Loss

Author

Listed:
  • David E. A. Giles

Abstract

In this paper, we consider a simple preliminary-test estimation problem where the analyst's loss structure is represented by a ‘reflected Normal' penalty function. In particular we consider the estimation of the location parameter in a Normal sampling problem, where a preliminary test is conducted for the validity of a simple restriction on this parameter. The exact finite-sample risk of this pre-test estimator is derived under ‘reflected Normal' loss, and this risk is compared with those of the unrestricted and restricted Maximum Likelihood estimators of location under this loss structure. The paper draws comparisons between these results and those obtained under conventional quadratic loss. Some simple Bayesian analysis is also considered. The results extend naturally to the case of estimating the coefficients in a Normal linear multiple regression model.

Suggested Citation

  • David E. A. Giles, 2000. "Preliminary-Test and Bayes Estimation of a Location Parameter Under 'Reflected Normal' Loss," Econometrics Working Papers 0004, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0004
    Note: ISSN 1485-6441
    as

    Download full text from publisher

    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0004.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Giles, David E. A. & Srivastava, Virendra K., 1993. "The exact distribution of a least squares regression coefficient estimator after a preliminary t-test," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 59-64, January.
    2. Giles, Judith A & Giles, David E A, 1993. "Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-197, June.
    3. Giles, Judith A., 1991. "Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances," Journal of Econometrics, Elsevier, vol. 50(3), pages 377-398, December.
    4. Giles, David E. A., 1993. "Pre-test estimation in regression under absolute error loss," Economics Letters, Elsevier, vol. 41(4), pages 339-343.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Bayes Estimators, Loss Functions, and J. M. Keynes
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-11 22:20:00

    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. Clarke, Judith A., 2008. "On weighted estimation in linear regression in the presence of parameter uncertainty," Economics Letters, Elsevier, vol. 100(1), pages 1-3, July.
    2. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2007. "A Monte Carlo Study for Pure and Pretest Estimators of a Panel Data Model with Spatially Autocorrelated Disturbances," Annals of Economics and Statistics, GENES, issue 87-88, pages 11-38.
    3. Ohtani, Kazuhiro, 1996. "Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 191-199, September.
    4. Peter M. Mphekgwana & Yehenew G. Kifle & Chioneso S. Marange, 2024. "Shrinkage Testimator for the Common Mean of Several Univariate Normal Populations," Mathematics, MDPI, vol. 12(7), pages 1-18, April.
    5. Danilov, D.L. & Magnus, J.R., 2002. "Estimation of the Mean of a Univariate Normal Distribution When the Variance is not Known," Discussion Paper 2002-77, Tilburg University, Center for Economic Research.
    6. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    7. Reif, Jiri & Vlcek, Karel, 2002. "Optimal pre-test estimators in regression," Journal of Econometrics, Elsevier, vol. 110(1), pages 91-102, September.
    8. Matei Demetrescu & Uwe Hassler & Vladimir Kuzin, 2011. "Pitfalls of post-model-selection testing: experimental quantification," Empirical Economics, Springer, vol. 40(2), pages 359-372, April.
    9. Wan, Alan T. K. & Zou, Guohua, 2003. "Optimal critical values of pre-tests when estimating the regression error variance: analytical findings under a general loss structure," Journal of Econometrics, Elsevier, vol. 114(1), pages 165-196, May.
    10. Yannick Hoga, 2022. "Quantifying the data-dredging bias in structural break tests," Statistical Papers, Springer, vol. 63(1), pages 143-155, February.
    11. Danilov, D.L. & Magnus, J.R., 2001. "On the Harm that Pretesting Does," Other publications TiSEM f131c709-4db4-468d-9ae8-9, Tilburg University, School of Economics and Management.
    12. S. K. Sapra, 2003. "Pre-test estimation in Poisson regression model," Applied Economics Letters, Taylor & Francis Journals, vol. 10(9), pages 541-543.
    13. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
    14. Akio Namba, 2001. "MSE performance of the 2SHI estimator in a regression model with multivariate t error terms," Statistical Papers, Springer, vol. 42(1), pages 81-96, January.
    15. Zou, Guohua & Wan, Alan T.K. & Wu, Xiaoyong & Chen, Ti, 2007. "Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 803-810, April.
    16. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    17. Lauren Bin Dong, 2004. "The Behrens-Fisher Problem: An Empirical Likelihood Ratio Approach," Econometrics Working Papers 0404, Department of Economics, University of Victoria.
    18. Wang, Song-Gui & Ip, Wai-Cheung, 2003. "Inconsistency of estimate of the degree of freedom of multivariate student-t disturbances in linear regression models," Economics Letters, Elsevier, vol. 80(3), pages 383-389, September.
    19. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.
    20. Lauren Bin Dong, 2004. "Testing for structural Change in Regression: An Empirical Likelihood Ratio Approach," Econometrics Working Papers 0405, Department of Economics, University of Victoria.

    More about this item

    Keywords

    preliminary testing; risk function; Bayes estimation;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:vic:vicewp:0004. 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: Kali Moon (email available below). General contact details of provider: https://edirc.repec.org/data/devicca.html .

    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.