Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
复制标题
DOI：
10.1146/annurev-economics-012315-015826
复制
发表时间：
2015-01-01
期刊：
影响因子：
--
通讯作者：
Spindler, Martin
中科院分区：
文献类型：
--
作者：
Chernozhukov, Victor;Hansen, Christian;Spindler, Martin
在高维干扰参数存在的情况下，我们给出了关于低维目标参数的有效的后选择或后正则化推断的说明性、一般性分析，该参数是使用选择或正则化方法估计的。我们的分析提供了一组高级条件，在这些条件下，尽管高维干扰参数的估计存在选择或正则化偏差，但基于测试或点估计方法的低维参数的推断将是规则的。一个关键因素是使用所谓的免疫或正交估计方程，这些方程对高维干扰参数估计中的小错误在局部不敏感。作为说明，我们分析了仿射-二次模型，并将这些结果特化为具有多个回归变量和多个工具的线性工具变量模型。最后，我们回顾了选择后推理的其他发展，并注意到许多可以被视为本文所提供的正交化估计方程的一般包罗万象框架的特例。
We present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter in the presence of a very high-dimensional nuisance parameter that is estimated using selection or regularization methods. Our analysis provides a set of high-level conditions under which inference for the low-dimensional parameter based on testing or point estimation methods will be regular despite selection or regularization biases occurring in the estimation of the high-dimensional nuisance parameter. A key element is the use of so-called immunized or orthogonal estimating equations that are locally insensitive to small mistakes in the estimation of the high-dimensional nuisance parameter. As an illustration, we analyze affine-quadratic models and specialize these results to a linear instrumental variables model with many regressors and many instruments. We conclude with a review of other developments in post-selection inference and note that many can be viewed as special cases of the general encompassing framework of orthogonal estimating equations provided in this article.