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Properties of the ordinary least squares and stein-rule predictions in linear regression models with proxy variables

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Abstract

This article considers a linear regression model in which misspecification relates to the use of a stochastic proxy variable. The analysis indicates the decline in efficiency of the predictions arising from the ordinary least squares and the Stein-rule estimation procedures when a proxy variable is used in the place of an unobservable variable. However, the performance of the Stein-rule predictions is still found to be better than the ordinary least squares predictions over a broad range of k, the characterizing scalar of the Stein-rule estimator.

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Authors and Affiliations

  1. Department of Statistics, Lucknow University, 226007, Lucknow, INDIA

    V. K. Srivastava

  2. Department of Statistics, Maharshi Dayanand University, 124001, Rohtak, INDIA

    M. Dube

Authors
  1. V. K. Srivastava
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  2. M. Dube
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Srivastava, V.K., Dube, M. Properties of the ordinary least squares and stein-rule predictions in linear regression models with proxy variables. Statistical Papers 34, 27–41 (1993). https://doi.org/10.1007/BF02925525

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  • DOI: https://doi.org/10.1007/BF02925525

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