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ISIPTA'09 -
SIXTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Durham University, Department of Mathematical Sciences

Durham, United Kingdom

Tuesday 14 to Saturday 18 July 2009

## ELECTRONIC PROCEEDINGS

## Robert Hable

# A Minimum Distance Estimator in an Imprecise Probability Model - Computational Aspects and Applications

### Abstract

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

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