Random Sets in Econometrics

Ilya Molchanov is Professor of Probability at the Universität Bern, Switzerland, having previously worked in Germany, the Netherlands and Scotland. His research and publications focus on probability theory, spatial statistics, and mathematical finance, with the main emphasis on stochastic geometry and the theory of random sets. Francesca Molinari is the H. T. Warshow and Robert Irving Warshow Professor of Economics at Cornell University, New York. She is a specialist in econometric theory, with emphasis on partial identification. She authored numerous papers in this area, including empirical ones on estimation of risk preferences using property insurance data.

• 1. Basic concepts; 2. Selections; 3. Expectation of random sets; 4. Limit theorems for Minkowski sums; 5. Estimation and interference.

'The book builds upon and greatly elaborates on the pioneering, fundamental work that Arie Beresteanu, Ilya Molchanov, and Francesca Molinari did on connecting econometric models with missing data and set-valued responses - such as games with multiple equilibria - to the theory of random sets, a beautiful field of mathematics, probability theory, and mathematical economics. It should be of equal interest to students and researchers in mathematical statistics, econometrics, and machine learning, particularly in problems where set-valued predictions arise, in either observational or counterfactual settings.' V. Chernozhukov, Economics Department and Center for Statistics and Data Science, Massachusetts Institute of Technology