Optimal Inference in a Class of Regression Models
Optimal Inference in a Class of Regression Models
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DOI：
10.3982/ecta14434
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发表时间：
2018-03-01
期刊：
影响因子：
6.1
通讯作者：
Kolesar, Michal
中科院分区：
文献类型：
--
作者：
Armstrong, Timothy B.;Kolesar, Michal
我们考虑了一个回归函数的线性泛函的置信区间（ci）的构造问题，如它在某一点的值，回归不连续参数，或线性或部分线性回归中的回归系数。我们的主要假设是回归函数已知位于凸函数类中，它涵盖了计量经济学中使用的大多数平滑和/或形状假设。在已知方差的正态误差下，导出了有限样本最优ci和尖锐效率界。我们表明，当误差分布未知时，这些结果转化为一致的（在函数类上）渐近结果。当函数类是中心对称的时，这些效率界意味着极小极大ci在光滑回归函数中接近效率。这尤其意味着，不可能使用依赖于数据的调优参数来形成实质上更紧凑的ci，并保持对整个函数类的覆盖。我们将我们的结果专门用于对回归不连续参数的推断，并在模拟和经验应用中加以说明。
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply that minimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are substantively tighter using data-dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference on the regression discontinuity parameter, and illustrate them in simulations and an empirical application.