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Prior-Free Probabilistic Inference for Econometricians

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Robustness in Econometrics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 692))

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Abstract

The econometrics literature is dominated by the frequentist school which places primary emphasis on the specification of methods that have certain long-run frequency properties, mostly disavowing any notion of inference based on the given data. This preference for frequentism is at least partially based on the belief that probabilistic inference is possible only through a Bayesian approach, the success of which generally depends on the unrealistic assumption that the prior distribution is meaningful in some way. This paper is intended to inform econometricians that an alternative inferential model (IM) approach exists that can achieve probabilistic inference without a prior and while enjoying certain calibration properties essential for reproducibility, etc. Details about the IM construction and its properties are presented, along with some intuition and examples.

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Notes

  1. 1.

    At his keynote address for a workshop on foundations at Rutgers University in April 2016, http://statistics.rutgers.edu/bff2016.

  2. 2.

    This is not an ideal choice of word because “predict” has a particular meaning in statistics and econometrics, but the meaning here is different. “Guess” or “impute” are other potential words to describe the operation in consideration, but both still miss the mark slightly. A more accurate description of what I have in mind is “to cast a net” at the target.

  3. 3.

    The formula (5) silently assumes that \(\varTheta _y(\mathcal {S})\) is non-empty with \(\mathsf {P}_\mathcal {S}\)-probability 1 for all y. This holds automatically in many cases, often because of the preprocessing discussed in Sect. 3, but not in all. The ideal remedy seems to be choosing a predictive random set which is elastic in a certain sense; see Ermini Leaf and Liu [12].

  4. 4.

    http://www.nature.com/nature/focus/reproducibility/index.html.

  5. 5.

    http://amstat.tandfonline.com/doi/abs/10.1080/00031305.2016.1154108.

  6. 6.

    Efficiency is essentially the rival to validity, and the goal is to balance between the two. For example, a belief function that always takes value 0 for all \(A \ne \varTheta \), which is achieved by a choosing an extreme predictive random set \(\mathcal {S}\equiv \mathbb {U}\), is sure to be valid, but then the corresponding plausibility function would always be 1; consequently, the plausibility regions would be unbounded and practically useless. So, roughly, the idea behind efficiency is to have the smallest predictive random set such that the IM is still efficient. More on this in Sect. 5.

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Acknowledgements

The author thanks the organizers of the 10th International Conference of the Thailand Econometric Society, in particular, Professor Hung Nguyen, for the invitation to present at the conference and to submit a paper for the proceedings.

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Authors and Affiliations

  1. Department of Statistics, North Carolina State University, 2311 Stinson Drive, Campus Box 8203, Raliegh, NC, 27695, USA

    Ryan Martin

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Correspondence to Ryan Martin .

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Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso Department of Computer Science, El Paso, TX, USA

    Vladik Kreinovich

  2. Faculty of Economics, Chiang Mai University Faculty of Economics, Chiang Mai, Thailand

    Songsak Sriboonchitta

  3. Japan Adv. Inst. of Sci. & Tech. (JAIST) , Ishikawa, Japan

    Van-Nam Huynh

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Martin, R. (2017). Prior-Free Probabilistic Inference for Econometricians. In: Kreinovich, V., Sriboonchitta, S., Huynh, VN. (eds) Robustness in Econometrics. Studies in Computational Intelligence, vol 692. Springer, Cham. https://doi.org/10.1007/978-3-319-50742-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-50742-2_10

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