摘要翻译：
本文对有关非参数工具变量(NPIV)的估计和结构函数$H_0$及其泛函的推断的文献作了一些重要的贡献。首先，我们得到了计算简单的筛NPIV（级数2SLS)估计的超范数收敛速度。其次，我们导出了一个描述估计$H0$及其导数的最佳可能（极小极大）超范数率的下界，并证明了当用样条或小波筛逼近$H0$时，筛NPIV估计器可以达到极小极大率。对于严重不适定问题，我们的最优超范数速率与最优均方根速率惊人地一致，而对于轻度不适定问题，我们的最优超范数速率只是比最优均方根速率慢的一个对数因子。第三，在本原条件下，我们利用超范数率建立了$H_0$非线性泛函集合的一致高斯过程强逼近和分数bootstrap一致置信带(UCBs)，允许轻度和严重不适定问题。第四，作为应用，我们得到了在低水平条件下，用筛子NPIV估计需求时，精确消费者剩余(CS)和自重损失(DL)福利泛函的插入筛子T-统计量的第一个渐近逐点一致推理结果。经验主义者可以阅读UCBs的真实数据应用，以获得汽油需求的精确CS和DL函数，这些函数揭示了有趣的模式，并适用于其他市场。
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英文标题：
《Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of
  Nonparametric IV Regression》
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作者：
Xiaohong Chen and Timothy M. Christensen
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最新提交年份：
2017
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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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英文摘要：
  This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when $h_0$ is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence bands (UCBs) for collections of nonlinear functionals of $h_0$ under primitive conditions, allowing for mildly and severely ill-posed problems. Fourth, as applications, we obtain the first asymptotic pointwise and uniform inference results for plug-in sieve t-statistics of exact consumer surplus (CS) and deadweight loss (DL) welfare functionals under low-level conditions when demand is estimated via sieve NPIV. Empiricists could read our real data application of UCBs for exact CS and DL functionals of gasoline demand that reveals interesting patterns and is applicable to other markets.
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PDF链接：
https://arxiv.org/pdf/1508.03365