Intersection Bounds: Estimation and Inference
提出一种实用的新方法，用于推断由参数或非参数函数的下确界或上确界定义的边界，特别适用于条件矩不等式下的参数边界估计，并提供了中位数偏差校正估计量。
We develop a practical and novel method for inference on intersection bounds,\nnamely bounds defined by either the infimum or supremum of a parametric or\nnonparametric function, or equivalently, the value of a linear programming\nproblem with a potentially infinite constraint set. We show that many bounds\ncharacterizations in econometrics, for instance bounds on parameters under\nconditional moment inequalities, can be formulated as intersection bounds. Our\napproach is especially convenient for models comprised of a continuum of\ninequalities that are separable in parameters, and also applies to models with\ninequalities that are non-separable in parameters. Since analog estimators for\nintersection bounds can be severely biased in finite samples, routinely\nunderestimating the size of the identified set, we also offer a\nmedian-bias-corrected estimator of such bounds as a by-product of our\ninferential procedures. We develop theory for large sample inference based on\nthe strong approximation of a sequence of series or kernel-based empirical\nprocesses by a sequence of "penultimate" Gaussian processes. These penultimate\nprocesses are generally not weakly convergent, and thus non-Donsker. Our\ntheoretical results establish that we can nonetheless perform asymptotically\nvalid inference based on these processes. Our construction also provides new\nadaptive inequality/moment selection methods. We provide conditions for the use\nof nonparametric kernel and series estimators, including a novel result that\nestablishes strong approximation for any general series estimator admitting\nlinearization, which may be of independent interest.\n