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2017 | OriginalPaper | Chapter

Prior-Free Probabilistic Inference for Econometricians

Author : Ryan Martin

Published in: Robustness in Econometrics

Publisher: Springer International Publishing

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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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previous chapter Weighted Least Squares and Adaptive Least Squares: Further Empirical Evidence

next chapter Robustness in Forecasting Future Liabilities in Insurance

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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.

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].

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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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Title: Prior-Free Probabilistic Inference for Econometricians
Author: Ryan Martin
Publisher: Springer International Publishing
Book: Robustness in Econometrics
Print ISBN: 978-3-319-50741-5

Electronic ISBN: 978-3-319-50742-2

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-50742-2_10

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