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Estimation of the mean of a univariate normal distribution when the variance is not known

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Author Info
Danilov, D. (Tilburg University, Center for Economic Research)
Abstract

We consider the problem of estimating the first k coeffcients in a regression equation with k + 1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We investigate properties of this estimator in the case where the unknown variance is estimated by least squares. We find that the optimality properties of the Laplace estimator only change marginally. Therefore we recommend the neutral Laplace estimator to be used in practice.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 77.

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Date of creation: 2002
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Handle: RePEc:dgr:kubcen:200277

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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  1. Judge, G.G. & Bock, M.E., 1983. "Biased estimation," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 10, pages 599-649 Elsevier. [Downloadable!] (restricted)
  2. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June. [Downloadable!] (restricted)
  3. Toyoda, Toshihsa & Wallace, T D, 1976. "Optimal Critical Values for Pre-Testing in Regression," Econometrica, Econometric Society, vol. 44(2), pages 365-75, March. [Downloadable!] (restricted)
  4. Giles, Judith A & Giles, David E A, 1993. " Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Blackwell Publishing, vol. 7(2), pages 145-97, June.
  5. Sawa, Takamitsu & Hiromatsu, Takeshi, 1973. "Minimax Regret Significance Points for a Preliminary Test in Regression Analysis," Econometrica, Econometric Society, vol. 41(6), pages 1093-1101, November. [Downloadable!] (restricted)
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