Stochastic Programming and Statistical Estimates

Abstract

The paper aims at drawing attention to the potential of (qualitative) stability theory of stochastic programming for the study of asymptotic properties of statistical estimates. Making use of existing stability results, it is often possible to weaken the assumptions and to deal also with non-standard estimation problems. Thus non-unique solutions to the underlying optimization problems as well as constraints for the estimates can be taken into account and the continuity assumptions can often be replaced by semicontinuity. In this paper the focus is on consistency for constrained estimation with non-unique solutions. It will be shown how stability results obtained by the author can be employed to derived assertions on the convergence in probability of statistical estimates. The general results use the epi-convergence approach.KeywordsStochastic ProgrammingLimit ProblemDeterministic SettingSurrogate ProblemContinuous ConvergenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.