Intersection Bounds: Estimation and Inference
交集界的估计与推断AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要提供通用交集界与条件矩不等式理论，未明确对应所列特定应用领域。
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交集界的估计与推断
- 研究问题
- 当参数界由一组函数的上确界或下确界决定时，如何修正直接代入估计造成的偏差，并对可能含无限约束的界进行推断？
- 方法与思路
- 作者以高斯过程强逼近处理级数或核经验过程，构造渐近推断、自适应不等式选择方法及中位数偏差修正的界估计。
- 材料陈述的贡献
- 摘要称即使逼近过程不具通常弱收敛性质，仍可开展有效渐近推断，并提供适用于可线性化一般级数估计量的强逼近结果。
- 阅读关注点
- 应核对上确界与下确界的符号约定、偏差修正及约束选择步骤，以及核和级数估计的平滑性、复杂度与强逼近条件。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或接收；摘要未说明具体误差率、调参规则及应用结果，不能判断有限样本覆盖率。
原文摘要
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.