多矩部分辨识模型的子向量推理 不等式

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摘要翻译：
本文讨论了部分辨识模型中参数向量函数的推论问题。这个框架允许矩条件的数量随着样本量增长，可能以指数速度增长。我们主要的激励应用是子向量推理，即对与治疗效果或感兴趣的策略变量相关的部分识别参数向量的单个分量进行推理。我们的推理方法将最小最大测试统计量（满足$H_0$和最大矩不等式的参数上的最小值）与基于bootstrap近似或解析界的临界值进行比较。我们证明了该方法在一大类数据生成过程中一致控制渐近大小，尽管存在部分识别的多矩不等式设置。有限样本分析允许我们获得关于尺寸控制的显式收敛速度。我们的结果是基于非渐近逼近和新的高维中心极限定理相结合的随机矩阵分量的极大值。与以前关于部分识别模型中的函数推理的文献不同，我们的结果不依赖于基于Donsker类假设的弱收敛结果，事实上，我们的检验统计量甚至可能在分布上不收敛。我们的bootstrap近似需要选择一个可以避免测试统计量过度集中的调优参数序列。为此，我们提出了一种渐近有效的数据驱动方法来选择这个调谐参数序列。该方法将调谐参数序列的选择推广到Donsker类假设之外的问题，也可能具有独立的兴趣。我们的程序基于自归一化的适度偏差范围，相对来说更保守，但更容易实现。
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英文标题：
《Subvector Inference in Partially Identified Models with Many Moment
  Inequalities》
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作者：
Alexandre Belloni, Federico Bugni and Victor Chernozhukov
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

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英文摘要：
  This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential rates. Our main motivating application is subvector inference, i.e., inference on a single component of the partially identified parameter vector associated with a treatment effect or a policy variable of interest.   Our inference method compares a MinMax test statistic (minimum over parameters satisfying $H_0$ and maximum over moment inequalities) against critical values that are based on bootstrap approximations or analytical bounds. We show that this method controls asymptotic size uniformly over a large class of data generating processes despite the partially identified many moment inequality setting. The finite sample analysis allows us to obtain explicit rates of convergence on the size control. Our results are based on combining non-asymptotic approximations and new high-dimensional central limit theorems for the MinMax of the components of random matrices. Unlike the previous literature on functional inference in partially identified models, our results do not rely on weak convergence results based on Donsker's class assumptions and, in fact, our test statistic may not even converge in distribution. Our bootstrap approximation requires the choice of a tuning parameter sequence that can avoid the excessive concentration of our test statistic. To this end, we propose an asymptotically valid data-driven method to select this tuning parameter sequence. This method generalizes the selection of tuning parameter sequences to problems outside the Donsker's class assumptions and may also be of independent interest. Our procedures based on self-normalized moderate deviation bounds are relatively more conservative but easier to implement.
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PDF链接：
https://arxiv.org/pdf/1806.11466

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关键词：不等式 inequalities econometrics distribution Conservative bootstrap 向量 收敛 部分 增长