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

Listed author(s):
  • 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.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0004.

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Length: 18 pages
Date of creation: 26 Apr 2000
Handle: RePEc:vic:vicewp:0004
Note: ISSN 1485-6441
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  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.
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