Continuous indetermination and average likelihood minimization
Information Theory
2021-05-05 v1 math.IT
Probability
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2105.01348,
title = {Continuous indetermination and average likelihood minimization},
author = {Pierre Bertrand and Michel Broniatowski and Jean-François Marcotorchino},
journal= {arXiv preprint arXiv:2105.01348},
year = {2021}
}