Collaborative Research: Honest Inference and Efficiency Bounds for Nonparametric Regression and Approximate Moment Condition Models

在分析经济数据时，研究人员使用的模型和假设通常最好被认为是对现实的近似。 这个项目将开发统计方法，当这些模型只是近似正确时，而不是完全正确。 本项目中开发的方法也可用于提供简单的方法，以评估实证研究结论对其基本假设的敏感性。 这些方法可以应用于许多与政策和理解经济相关的常用研究问题。本项目将开发具有凸参数空间的近似矩条件模型的置信区间，以及表明它们在某种精确意义上尽可能紧密的尖锐效率界。该设置涵盖了对非参数回归函数的线性泛函的推断，例如其在一个点的值，回归不连续参数，或未混淆下的平均治疗效果。该设置还涵盖了线性回归模型中的参数约束以及矩条件模型，例如广义矩量法（GMM）或矩条件局部错误指定的最小距离模型。置信区间构造简单，并且在“诚实”或统一的意义上有效。作为结果的特殊情况，该项目获得了非参数回归模型中的最优推理核，以及错误设定下GMM的最优权重。

In analyzing economic data, researchers use models and assumptions that are typically best thought of as approximations of reality. This project will develop statistical methods that are valid when these models are only approximately correct, rather than exactly correct. The methods developed in this project can also be used to provide simple ways of assessing the sensitivity of the conclusions of an empirical study to its underlying assumptions. These methods can be applied to numerous commonly studied problems that are relevant for policy and for understanding the economy.This project will develop confidence intervals in approximate moment condition models with convex parameter spaces, as well as sharp efficiency bounds showing that they are as tight as possible in a certain precise sense. The setup covers inference on a linear functional of a nonparametric regression function, such as its value at a point, the regression discontinuity parameter, or an average treatment effect under unconfoundedness. The setup also covers parameter constraints in the linear regression model as well as moment condition models such as generalized method of moments (GMM) or minimum distance models in which the moment condition is locally misspecified. The confidence intervals are simple to construct, and valid in an "honest" or uniform sense. As special cases of the results, the project obtains optimal kernels for inference in nonparametric regression models, and optimal weights for GMM under misspecification.