Minimum distance estimation in imprecise probability models

The present article considers estimating a parameter θθ in an imprecise probability model (P¯θ)θ∈Θ. This model consists of coherent upper previsions P¯θ which are given by finite numbers of constraints on expectations. A minimum distance estimator is defined in this case and its asymptotic properties are investigated. It is shown that the minimum distance can be approximately calculated by discretizing the sample space. Finally, the estimator is applied in a simulation study and on a real data set.