摘要翻译：
在非参数工具变量模型中恢复回归函数的逆问题的不适定性导致估计量可能遭受非常慢的对数收敛速度。在本文中，我们证明了将问题限制在具有单调回归函数和单调工具的模型上，显著地削弱了问题的不适定性。与现有文献形成鲜明对比的是，单调工具的存在意味着我们的不适定性测度在局限于单调函数空间时的有界性。在此基础上，我们给出了约束估计的一个新的非渐近误差界。对于给定的样本量，只要回归函数不太陡，其界与不适定性无关。作为一个蕴涵，这个界允许我们证明约束估计量在常数函数的一个大的但缓慢收缩的邻域中以快速的多项式速度收敛，而与不适定性无关。我们的模拟研究表明，即使在回归函数远不是常数的情况下，施加单调性也能显著地提高有限样本的性能。我们将约束估计量应用于从美国数据估计汽油需求函数的问题。
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英文标题：
《Nonparametric instrumental variable estimation under monotonicity》
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作者：
Denis Chetverikov and Daniel Wilhelm
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最新提交年份：
2015
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分类信息：

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：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：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：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：
  The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem. In stark contrast to the existing literature, the presence of a monotone instrument implies boundedness of our measure of ill-posedness when restricted to the space of monotone functions. Based on this result we derive a novel non-asymptotic error bound for the constrained estimator that imposes monotonicity of the regression function. For a given sample size, the bound is independent of the degree of ill-posedness as long as the regression function is not too steep. As an implication, the bound allows us to show that the constrained estimator converges at a fast, polynomial rate, independently of the degree of ill-posedness, in a large, but slowly shrinking neighborhood of constant functions. Our simulation study demonstrates significant finite-sample performance gains from imposing monotonicity even when the regression function is rather far from being a constant. We apply the constrained estimator to the problem of estimating gasoline demand functions from U.S. data.
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PDF链接：
https://arxiv.org/pdf/1507.05270