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


  • David E. A. Giles



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

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    References listed on IDEAS

    1. 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.
    2. Giles, David E. A., 1993. "Pre-test estimation in regression under absolute error loss," Economics Letters, Elsevier, vol. 41(4), pages 339-343.
    3. 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.
    4. 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.
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    Blog mentions

    As found by, 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

    More about this item


    preliminary testing; risk function; Bayes estimation;

    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

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