
Parameter estimation with a class of outer probability measures
We explore the interplay between random and deterministic phenomena usin...
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Expectile based measures of skewness
In the literature, quite a few measures have been proposed for quantifyi...
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Algorithmically Optimal Outer Measures
We investigate the relationship between algorithmic fractal dimensions a...
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Minimum divergence estimators, Maximum Likelihood and the generalized bootstrap
This paper is an attempt to set a justification for making use of some d...
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Optimal Nested Simulation Experiment Design via Likelihood Ratio Method
Nested simulation arises frequently in financial or input uncertainty qu...
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An exposition of the false confidence theorem
A recent paper presents the "false confidence theorem" (FCT) which has p...
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Empirical Likelihood Under Misspecification: Degeneracies and Random Critical Points
We investigate empirical likelihood obtained from misspecified (i.e. bi...
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Elements of asymptotic theory with outer probability measures
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as estimation or hypothesis testing need to be analysed in order to understand their behaviour, and motivate their use. In this article, we consider a simple class of outer measures based on the supremum of particular functions that we refer to as possibility functions. We then derive the asymptotic properties of the corresponding maximum likelihood estimators, likelihood ratio tests and Bayesian posterior uncertainties. These results are largely based on versions of both the law of large numbers and the central limit theorem that are adapted to possibility functions. Our motivation with outer measures is through the notion of uncertainty quantification, where verification of these procedures is of crucial importance. These introduced concepts naturally strengthen the link between the frequentist and Bayesian approaches.
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