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Estimation of the mean of a univariate normal distribution with known variance

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  • Jan R. Magnus

    () (CentER, Tilburg University, The Netherlands)

Abstract

We consider the estimation of the unknown mean "&eegr;" of a univariate normal distribution N("&eegr;", 1) given a single observation "x". We wish to obtain an estimator which is admissible and has good risk (and regret) properties. We first argue that the "usual" estimator "t" ("x") = "x" is not necessarily suitable. Next, we show that the traditional pretest estimator of the mean has many undesirable properties. Thus motivated, we suggest the Laplace estimator, based on a "neutral" prior for "&eegr;", and obtain its properties. Finally, we compare the Laplace estimator with a large class of (inadmissible) estimators and show that the risk properties of the Laplace estimator are close to those of the minimax regret estimator from this large class. Thus, the Laplace estimator has good risk (regret) properties as well. Questions of admissibility, risk and regret are reviewed in the appendix. Copyright Royal Economic Society 2002

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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 5 (2002)
Issue (Month): 1 (June)
Pages: 225-236

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Handle: RePEc:ect:emjrnl:v:5:y:2002:i:1:p:225-236

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Cited by:
  1. Magnus, J.R. & Wang, W. & Zhang, Xinyu, 2012. "WALS Prediction," Discussion Paper 2012-043, Tilburg University, Center for Economic Research.
  2. 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.
  3. 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.
  4. Reif, Jiri, 2007. "Asymptotic behaviour of regression pre-test estimators with minimal Bayes risk," Journal of Econometrics, Elsevier, vol. 140(2), pages 413-424, October.
  5. De Luca, G. & Magnus, J.R., 2011. "Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues," Discussion Paper 2011-082, Tilburg University, Center for Economic Research.
  6. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
  7. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2011. "A Generalized Missing-Indicator Approach to Regression with Imputed Covariates," EIEF Working Papers Series 1111, Einaudi Institute for Economic and Finance (EIEF), revised May 2011.
  8. Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.
  9. Magnus, J.R. & Powell, O.R. & Prüfer, P., 2008. "A Comparison of Two Averaging Techniques with an Application to Growth Empirics," Discussion Paper 2008-39, Tilburg University, Center for Economic Research.
  10. Magnus, Jan R. & Wan, Alan T.K. & Zhang, Xinyu, 2011. "Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1331-1341, March.
  11. Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  12. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.

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