SYMMETRIC CONFIDENCE REGIONS AND CONFIDENCE INTERVALS FOR NORMAL MAP FORMULATIONS OF STOCHASTIC VARIATIONAL INEQUALITIES
SYMMETRIC CONFIDENCE REGIONS AND CONFIDENCE INTERVALS FOR NORMAL MAP FORMULATIONS OF STOCHASTIC VARIATIONAL INEQUALITIES
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DOI：
10.1137/13090506x
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发表时间：
2014-01-01
影响因子：
3.1
通讯作者：
Lu, Shu
中科院分区：
文献类型：
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作者：
Lu, Shu
随机变分不等式 (SVI) 对一大类受数据不确定性影响的均衡问题进行建模，并且与随机优化问题密切相关。 SVI 解通常通过样本平均近似 (SAA) 问题的解来估计。本文考虑了 SVI 的法线图公式，并提出了一种基于 SAA 解的渐近分布为法线图公式的解构建渐近精确置信区域和置信区间的方法。置信区域是高概率的单个椭球。我们还讨论了同时和单独置信区间的计算。
Stochastic variational inequalities (SVIs) model a large class of equilibrium problems subject to data uncertainty and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method for building asymptotically exact confidence regions and confidence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The confidence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual confidence intervals.