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A Maximum Likelihood Approach to Inference Under Coarse Data Based on Minimax Regret

Guillaume, Romain and Dubois, Didier A Maximum Likelihood Approach to Inference Under Coarse Data Based on Minimax Regret. (2018) In: International Conference on Soft Methods in Probability and Statistics (SMPS 2018), 17 September 2018 - 21 September 2018 (Compiègne, France).

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Official URL: https://doi.org/10.1007/978-3-319-97547-4_14

Abstract

Various methods have been proposed to express and solve maximum likelihood problems with incomplete data. In some of these approaches, the idea is that incompleteness makes the likelihood function imprecise. Two proposals can be found to cope with this situation: maximize the maximal likelihood induced by precise datasets compatible with the incomplete observations, or maximize the minimal such likelihood. These approaches prove to be extremist, the maximax approach having a tendency to disambiguate the data, while the maximin approach favors uniform distributions. In this paper we propose an alternative approach consisting in minimax relative regret criterion with respect to maximal likelihood solutions obtained for all precise datasets compatible with the coarse data. It uses relative likelihood and seems to achieve a trade-off between the maximax and the maximin methods.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in volume 832 of Advances in Intelligent Systems and Computing book series ISSN: 2194-5357 ISBN 978-3-319-97546-7 The original PDF is available at: https://link.springer.com/chapter/10.1007%2F978-3-319-97547-4_14
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:22 May 2019 09:57

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