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Minimum distance estimation in imprecise probability models. (English) Zbl 1177.62028
Summary: The present article considers estimating a parameter \(\theta \) in an imprecise probability model \((\overline P_\theta)_{\theta \in \varTheta}\). This model consists of coherent upper previsions \(\overline P_\theta\) 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.

MSC:
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62F35 Robustness and adaptive procedures (parametric inference)
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
62G35 Nonparametric robustness
65C60 Computational problems in statistics (MSC2010)
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