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Bayesian Estimation of a Possibly Mis-Specified Linear Regression Model

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Abstract

We consider Bayesian estimation of the coefficients in a linear regression model, using a conjugate prior, when certain additional exact restrictions are placed on these coefficients. The bias and matrix mean squared errors of the Bayes and restricted Bayes estimators are compared when these restrictions are both true and false. These results are then used to determine the consequences of model mis-specification in terms of over-fitting or under-fitting the model. Our results can also be applied directly to determine the properties of the “ridge” regression estimator when the model may be mis-specified, and other such applications are also suggested.

Suggested Citation

  • David E. Giles, 2010. "Bayesian Estimation of a Possibly Mis-Specified Linear Regression Model," Econometrics Working Papers 1004, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:1004
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp1004.pdf
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    More about this item

    Keywords

    Bayes estimator; regression model; linear restrictions; model mis-specification; bias; matrix mean squared error;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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