Higher-Order Confidence Intervals for Stochastic Programming Using Bootstrapping

TitleHigher-Order Confidence Intervals for Stochastic Programming Using Bootstrapping
Publication TypeJournal Article
Year of Publication2011
AuthorsAnitescu, M, Petra, CG
Date Published10/2011
Other NumbersANL/MCS-P1964-1011
Abstract

We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization problem involving complex spatio- temporal uncertainty, for example coming from weather prediction. However, bootstrapping works provably better than traditional inference technique based on the central limit theorem only for parameters that are nite-dimensional and smooth functions of the moments, whereas the optimal value of the stochastic optimization problem is not. In this paper we propose and analyze a new bootstrap-based estimator for the optimal value that gives higher-order condence intervals.

PDFhttp://www.mcs.anl.gov/papers/P1964-1011.pdf