标题： 带有应用的广义最大值定理 显示英文标题

标题： A Generalized Argmax Theorem with Applications

摘要： argmax定理是许多应用中推导估计量极限分布的一个有用结果。 argmax定理的结论指出，一个随机过程序列的argmax在分布上收敛到一个极限随机过程的argmax。 本文将argmax定理推广，以允许在定义域的一系列子集上进行最大化。 如果这些子集的序列收敛到一个极限子集，那么argmax定理的结论仍然成立。 我们通过三个应用展示了这种推广的实用性：估计结构变化点，估计参数空间边界上的参数，以及估计弱识别参数。 广义的argmax定理简化了现有结果的证明，并可用于这些文献中证明新的结果。 显示英文摘要

摘要： The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to the argmax of a limiting stochastic process. This paper generalizes the argmax theorem to allow the maximization to take place over a sequence of subsets of the domain. If the sequence of subsets converges to a limiting subset, then the conclusion of the argmax theorem continues to hold. We demonstrate the usefulness of this generalization in three applications: estimating a structural break, estimating a parameter on the boundary of the parameter space, and estimating a weakly identified parameter. The generalized argmax theorem simplifies the proofs for existing results and can be used to prove new results in these literatures.