# FIDUCIAL THEORY AND OPTIMAL INFERENCE

@article{Taraldsen2013FIDUCIALTA, title={FIDUCIAL THEORY AND OPTIMAL INFERENCE}, author={Gunnar Taraldsen and Bo Henry Lindqvist}, journal={Annals of Statistics}, year={2013}, volume={41}, pages={323-341} }

It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and generalizes results corresponding to the choice of the right Haar measure as a Bayesian prior. Classical and more recent examples show that fiducial arguments can be used to give good candidates for exact or approximate confidence distributions. It is here suggested…

## 58 Citations

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The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is generalized here. For this the underlying probability space of Kolmogorov is replaced by…

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The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and…

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Generalized Fiducial Inference (GFI) is motivated by R.A. Fisher's approach of obtaining posterior-like distributions when there is no prior information available for the unknown parameter. Without…

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Abstract R. A. Fisher, the father of modern statistics, proposed the idea of fiducial inference during the first half of the 20th century. While his proposal led to interesting methods for…

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Starting around the year 2000, the authors and collaborators started to re-investigate the idea of ducial inference and discovered that Fisher's approach, when properly generalized, would open doors to solve many important and dicult inference problems.

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A generalization of the IM framework is proposed that is more flexible in that it does not require a complete specification of the data-generating process and provides an automatic auxiliary variable dimension reduction, which is valuable from an efficiency point of view.

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