This note considers the problem of constructing an asymptotically normal statistic for the value function of a convex stochastic minimization programme, which may have more than one minimizer. It introduces the proximal statistic using a recursive estimator of one of the minimizers. The use of this statistic is illustrated by extending an existing selection test for point-identifying parametric models to the set-identifying case

中文翻译：

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近端统计量：渐近正态性

本笔记考虑了为凸随机最小化程序的价值函数构建渐近正态统计量的问题，该程序可能有多个最小化器。它使用最小化器之一的递归估计器引入了近端统计量。通过将用于点识别参数模型的现有选择测试扩展到集合识别案例来说明此统计量的使用