ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 90 Fandom Noubiap, Roger, Humboldt-Universität zu Berlin A Minimax Algorithm for Calculating Statistical Tests Under Generalized Moment Conditions In decision theory, statistical tests subject to generalized moment conditions can be obtained as solution of two stage optimization problems of the form min_{n,c} sup_{π∈Γ} ∫_{Θ} R(n, c, θ)dπ(θ). One of the main difficulties here is the

maximization of the integral of the risk function over a set Γ of probability measures. We use the theory of linear semi-infinite optimization and exploit quasiconvexity properties of the outer minimization problem to construct a very efficient exact algorithm. Under a regularity condition, we prove the convergence of our algorithm. Numerical examples are reported. Ref. R. Fandom Noubiap, Discussion Papers in Statistics and Quantitative Economics, Universität der Bundeswehr Hamburg, 77, 81 (1997).