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A Generalized Argmax Theorem with Applications

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  • Gregory Cox
Abstract
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.

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  • Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    • Handle: RePEc:arx:papers:2209.08793
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    References listed on IDEAS

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    3. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
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    1. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2023. "Bootstrap-Assisted Inference for Generalized Grenander-type Estimators," Papers 2303.13598, arXiv.org, revised Jul 2024.

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