Summary: Noname manuscript No.
(will be inserted by the editor)
Higher-Order Confidence Intervals for Stochastic
Programming using Bootstrapping
Mihai Anitescu · Cosmin G. Petra
Received: date / Accepted: date
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 spatio-temporal 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 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 ·