摘要翻译：
本文讨论了用$P$表示的矩不等式数目可能远大于样本量$N$的多个矩不等式的检验问题。在许多经济应用中，解决这个问题可以对因果和结构参数进行推断，一个显著的例子是Ciliberto和Tamer(2009)的市场结构模型，其中$P=2^{m+1}$，$m$是可能进入市场的公司数量。我们考虑了由$P$studitized（或$T$type)不等式统计量的最大值所给出的检验统计量，并分析了计算检验统计量临界值的各种方法。具体地说，我们考虑的临界值基于(i)结合自归一化和的一个中等偏差不等式的并界，(ii)乘数和经验引导，(iii)两步和三步变式(i)和(ii)通过结合对远未绑定的无信息不等式的选择和对潜在绑定但不提供一阶信息的弱信息不等式的新选择。我们证明了这些方法的有效性，表明在温和的条件下，它们导致的测试的大小误差以$n$为单位多项式递减，同时允许$p$比$n$大得多，对于一些$c>0$,实际上$p$可以是$\exp(n^{c}）$级。重要的是，所有这些结果都不受p$研究统计量之间的相关结构的任何限制，并且对于适当大类的潜在分布也是一致的。此外，在在线补充中，我们在一些一般混合条件下，证明了基于块乘法器引导的测试在相依数据情况下的有效性。
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英文标题：
《Inference on causal and structural parameters using many moment
  inequalities》
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作者：
Victor Chernozhukov, Denis Chetverikov, and Kengo Kato
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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。
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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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 the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters, a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of $p$ Studentized (or $t$-type) inequality-specific statistics, and analyze various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in $n$ while allowing for $p$ being much larger than $n$, indeed $p$ can be of order $\exp (n^{c})$ for some $c > 0$. Importantly, all these results hold without any restriction on the correlation structure between $p$ Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.
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PDF链接：
https://arxiv.org/pdf/1312.7614