论文标题
具有应用程序的广义Argmax定理
A Generalized Argmax Theorem with Applications
论文作者
论文摘要
Argmax定理是在许多应用中得出估计器的限制分布的有用结果。 Argmax定理的结论指出，随机过程的一系列随机过程的argmax在分布中收敛到限制随机过程的Argmax。本文概括了Argmax定理，以使最大化发生在域的一系列子集上。如果子集的序列收敛到限制子集，则argmax定理的结论继续保持。我们证明了这种概括在三个应用程序中的有用性：估计结构断裂，估算参数空间边界的参数，并估算一个弱标识的参数。广义的Argmax定理简化了现有结果的证明，可以用来证明这些文献中的新结果。
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.
