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Estimation of Parameters in a Linear Regression Model under the Kullback-Leibler Loss

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Author Info

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • Hisayuki Tsukuma

    (Faculty of Medicine, Toho University)

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    Abstract

    This paper is concerned with the simultaneous estimation of parameters of regression coefficients and error variance in a linear regression model. Motivated from the Akaike information criterion, the expected Kullback-Leibler distance is employed as a risk function for comparing estimators in a decision-theoretic framework. This setup gives us the difficulty in handling the risk because an estimator of the variance is incorporated into the loss for estimating the regression coefficients. In this situation, several estimators of the variance and the regression coefficients are proposed and shown to improve on usual estimators used as a benchmark. Through simulation studies for the risk behavior of estimators, it is numerically shown that a truncated estimator has more favorable risk than the usual estimators.

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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-389.

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    Length: 28 pages
    Date of creation: Nov 2005
    Date of revision:
    Handle: RePEc:tky:fseres:2005cf389

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