A0528
Title: Minimax asymptotics
Authors: Mika Meitz - University of Helsinki (Finland) [presenting]
Alexander Shapiro - Georgia Institute of Technology (United States)
Abstract: Asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems are considered. Specifically, estimators of the optimal value and the optimal solutions are considered in a sample minimax problem that approximates the true population problem, and the limiting distributions of these estimators are studied, as the sample size tends to infinity. The main technical tool employed in the analysis is the theory of sensitivity analysis of parameterized mathematical optimization problems. Results go well beyond the existing literature and show that these limiting distributions are highly non-Gaussian in general and normal in simple specific cases. These results open up the way for the development of statistical inference methods in parametric minimax problems.
