Continuous indetermination and average likelihood minimization
Abstract
The authors transpose a discrete notion of indetermination coupling in the case of continuous probabilities. They show that this coupling, expressed on densities, cannot be captured by a specific copula which acts on cumulative distribution functions without a high dependence on the margins. Furthermore, they define a notion of average likelihood which extends the discrete notion of couple matchings and demonstrate it is minimal under indetermination. Eventually, they leverage this property to build up a statistical test to distinguish indetermination and estimate its efficiency using the Bahadur's slope.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.01348
- arXiv:
- arXiv:2105.01348
- Bibcode:
- 2021arXiv210501348B
- Keywords:
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- Computer Science - Information Theory;
- Mathematics - Probability;
- Mathematics - Statistics Theory