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A theory of dichotomous valuation with applications to variable selection

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  • Xingwei Hu

Abstract

An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables, we derive a valuation framework by the expected marginal gain and marginal loss in all potential modeling scenarios. However, marginal gain and loss are not symmetric; thus, we introduce three unbiased solutions. When used in variable selection, our new approaches significantly outperform several popular methods used in practice. The results also explore some novel traits of the Shapley value.

Suggested Citation

  • Xingwei Hu, 2020. "A theory of dichotomous valuation with applications to variable selection," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1075-1099, November.
    • Handle: RePEc:taf:emetrv:v:39:y:2020:i:10:p:1075-1099
    DOI: 10.1080/07474938.2020.1735750
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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