论文标题
随机优化的推断：自由午餐的引导程序
Inference by Stochastic Optimization: A Free-Lunch Bootstrap
论文作者
论文摘要
当渐近方差在分析上无法分析时，评估极值估计中的采样不确定性可能是具有挑战性的。 Bootstrap推理提供了可行的解决方案，但在计算上可能是昂贵的，尤其是在模型复杂时。本文使用特殊设计的随机优化算法的迭代术，如该算法，可以在单个运行中计算点估计值和Bootstrap标准误差。抽奖是由从每次迭代重新采样的数据批次计算出的梯度和黑森生成的。我们表明，对于大量的常规问题，这些抽奖产生一致的估计和无效的常见性推断。该算法在较低的计算成本中提供了模拟示例和经验应用中的准确标准错误。算法中的抽取还提供了一种方便的方法来检测数据不规则性。
Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model is complex. This paper uses iterates of a specially designed stochastic optimization algorithm as draws from which both point estimates and bootstrap standard errors can be computed in a single run. The draws are generated by the gradient and Hessian computed from batches of data that are resampled at each iteration. We show that these draws yield consistent estimates and asymptotically valid frequentist inference for a large class of regular problems. The algorithm provides accurate standard errors in simulation examples and empirical applications at low computational costs. The draws from the algorithm also provide a convenient way to detect data irregularities.
