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Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping

Mihai Anitescu (anitescu***at***mcs.anl.gov)
Cosmin Petra (petra***at***mcs.anl.gov)

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 finite-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 confidence intervals.

Keywords: Stochastic programming, Nonlinear programming, Bootstrap Exponential convergence

Category 1: Stochastic Programming

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Preprint ANL/MCS-P1964-1011

Download: [PDF]

Entry Submitted: 10/19/2011
Entry Accepted: 10/19/2011
Entry Last Modified: 12/14/2011

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