Molchanov, Ilya; Molinari, Francesca
(2014).
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Applications of random set theory in econometrics.
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Annual Review of Economics, 6(1), pp. 229-251.
10.1146/annurev-economics-080213-041205

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

## Item Type: |
Journal Article (Review Article) |
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## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |

## UniBE Contributor: |
Molchanov, Ilya |

## Subjects: |
500 Science > 510 Mathematics |

## Language: |
English |

## Submitter: |
Lutz Dümbgen |

## Date Deposited: |
25 Sep 2014 14:05 |

## Last Modified: |
08 Aug 2016 15:51 |

## Publisher DOI: |
10.1146/annurev-economics-080213-041205 |

## URI: |
https://boris.unibe.ch/id/eprint/57973 |