Optimal Inference in a Class of Regression Models
研究了在回归函数属于凸函数类时，如何构造线性泛函（如点值、断点回归参数）的最优置信区间，并推导了有限样本和渐近效率界，证明数据依赖调参无法缩小区间。
We consider the problem of constructing confidence intervals (CIs) for a\nlinear functional of a regression function, such as its value at a point, the\nregression discontinuity parameter, or a regression coefficient in a linear or\npartly linear regression. Our main assumption is that the regression function\nis known to lie in a convex function class, which covers most smoothness and/or\nshape assumptions used in econometrics. We derive finite-sample optimal CIs and\nsharp efficiency bounds under normal errors with known variance. We show that\nthese results translate to uniform (over the function class) asymptotic results\nwhen the error distribution is not known. When the function class is\ncentrosymmetric, these efficiency bounds imply that minimax CIs are close to\nefficient at smooth regression functions. This implies, in particular, that it\nis impossible to form CIs that are tighter using data-dependent tuning\nparameters, and maintain coverage over the whole function class. We specialize\nour results to inference on the regression discontinuity parameter, and\nillustrate them in simulations and an empirical application.\n