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The exact distribution and density functions of a pre-test estimator of the error variance in a linear regression model with proxy variables

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Abstract

We consider a linear regression model when some independent variables are unobservable, but proxy variables are available instead of them. We derive the distribution and density functions of a pre-test estimator of the error variance after a pre-test for the null hypothesis that the coefficients for the unobservable variables are zeros. Based on the density function, we show that when the critical value of the pre-test is unity, the coverage probability in the interval estimation of the error variance is maximum.

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Authors and Affiliations

  1. Department of Economics, Kobe University of Commerce, Gakuen Nishimari, Nishi-ku, 651-21, Kobe, Japan

    Hiroko Kurumai

  2. Faculty of Economics, Kobe University, Rokkodai, Nada-ku, 657, Kobe, Japan

    Kazuhiro Ohtani

Authors
  1. Hiroko Kurumai
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  2. Kazuhiro Ohtani
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Kurumai, H., Ohtani, K. The exact distribution and density functions of a pre-test estimator of the error variance in a linear regression model with proxy variables. Statistical Papers 39, 163–177 (1998). https://doi.org/10.1007/BF02925404

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  • DOI: https://doi.org/10.1007/BF02925404

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