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Estimation of the Mean of a Univariate Normal Distribution When the Variance is not Known

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  • Danilov, D.L.
  • Magnus, J.R.

    (Tilburg University, Center for Economic Research)

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    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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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2002-77.

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

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    Web page: http://center.uvt.nl

    Related research

    Keywords: regression analysis; estimation; statistical distribution; variance;

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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.
    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.
    3. Droge Bernd & Georg Thomas, 1995. "On Selecting The Smoothing Parameter Of Least Squares Regression Estimates Using The Minimax Regret Approach," Statistics & Risk Modeling, De Gruyter, vol. 13(1), pages 1-20, January.
    4. 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.
    5. Toyoda, Toshihsa & Wallace, T D, 1976. "Optimal Critical Values for Pre-Testing in Regression," Econometrica, Econometric Society, vol. 44(2), pages 365-75, March.
    6. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    7. 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 145-97, June.
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