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" Random sets in econometrics / "
Ilya Molchanov, Francesca Molinari.
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BL
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| Record Number
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839007
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| Main Entry
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Molchanov, Ilya S.,1962-
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| Title & Author
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Random sets in econometrics /\ Ilya Molchanov, Francesca Molinari.
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| Publication Statement
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Cambridge, United Kingdom ;New York, NY :: Cambridge University Press,, 2018.
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, ©2018
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| Series Statement
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Econometric Society monographic series ;; 60
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xvii, 178 pages :: illlustrations ;; 23 cm.
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| ISBN
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1107121205
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: 110754873X
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: 9781107121201
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: 9781107548732
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9781108650748 (PDF ebook)
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Includes bibliographical references and index.
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| Contents
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1. Basic concepts of random sets -- Random closed sets -- Hitting probabilities and the capacity functional -- Other functionals generated by random sets -- Capacities in game theory and economics -- 2. Selections -- Selections and measurability -- Characterization of selections -- Selections in econometrics: basic applications -- Adding extra structures to selections in econometrics -- 3. Expectation of random sets -- Selection expectation -- Support function and expectation -- Existence of selections with given moments -- Selection expectation in partial identification -- Other definitions of expectations -- 4. Limit theorems for Minkowski sums -- Minkowski addition -- Law of large numbers -- Central limit theorem -- Interference for the selection expectation -- Applications in partial identification -- Heavy tails -- 5. Estimation and inference -- Analysis basd on the empirical capacity functional -- Analysis based on inequalities involving other functionals -- Applications in partial identification -- Stationary random sets.
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| Abstract
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Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.
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| Subject
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Econometrics.
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Random sets.
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Econometrics.
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Random sets.
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| Dewey Classification
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330.01/5192
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| LC Classification
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HB139.M64 2018
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| Added Entry
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Molinari, Francesca
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