HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS
HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS
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非参数 IV 回归和其他不适定模型中的诚实置信度
DOI：
10.1017/s0266466619000380
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发表时间：
2016
影响因子：
0.8
通讯作者：
Andrii Babii
中科院分区：
文献类型：
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作者：
Andrii Babii
摘要：本文发展了计量经济学中一类非常普遍的不适定模型的推理方法，包括非参数工具变量回归、各种函数回归和密度反卷积。我们关注的是用Tikhonov正则化估计的感兴趣参数的统一置信集，如Darolles等人（2011,Econometrica 79, 1541-1565）。由于不可能有基于中心极限定理的推理方法，我们开发了两种依赖于浓度不等式和自举近似的替代方法。我们证明了结果集的期望直径和覆盖属性在一大类模型上具有一致的有效性，即构造的置信集是诚实的。蒙特卡罗实验表明，所引入的置信集具有合理的宽度和覆盖特性。使用美国的数据，我们为各种商品的恩格尔曲线提供了统一的置信集。
Abstract This article develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles et al. (2011, Econometrica 79, 1541–1565). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, that is, constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. Using U.S. data, we provide uniform confidence sets for Engel curves for various commodities.