 
Summary: Noname manuscript No.
(will be inserted by the editor)
HigherOrder Confidence Intervals for Stochastic
Programming using Bootstrapping
Mihai Anitescu · Cosmin G. Petra
Received: date / Accepted: date
Preprint ANL/MCSP19641011
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 un
known parameters for which only a small number of samples can be obtained.
One such parameter is the optimal value of a stochastic optimization prob
lem involving complex spatiotemporal uncertainty, for example coming from
weather prediction. However, bootstrapping works provably better than tra
ditional inference technique based on the central limit theorem only for pa
rameters that are finitedimensional 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 bootstrapbased estimator for the
optimal value that gives higherorder confidence intervals.
Keywords Stochastic programming · Nonlinear programming · Bootstrap ·
