The present article considers estimating a parameter $\theta$ in an imprecise probability model $(\overline{P}_{\theta})_{\theta\in\Theta}$ which consists of coherent upper previsions $\overline{P}_{\theta}$. After the definition of a minimum distance estimator in this setup and a summarization of its main properties, the focus lies on applications. It is shown that approximate minimum distances on the discretized sample space can be calculated by linear programming. After a discussion of some computational aspects, the estimator is applied in a simulation study consisting of two different models. Finally, the estimator is applied on a real data set in a linear regression model.
Keywords. Imprecise probabilities, coherent lower previsions, minimum distance estimator, empirical measure, R Project for Statistical Computing
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Authors addresses:
Department of Mathematics
University of Bayreuth
D-95440 Bayreuth
Germany
E-mail addresses:
| Robert Hable | Robert.Hable@uni-bayreuth.de |
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