EconBase
← All papers

A Generalized Argmax Theorem with Applications

Gregory Cox

arXiv 19 Sep 2022 · Econometrics · 1 citations (OpenAlex)

arXiv:2209.08793 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

44
references
89
in-text mentions
44
distinct cited
2
self-citations
8,737
main-text words

appendix boundary found by appendix_command · 61% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1van der Vaart, A. and Wellner, J (1996) Weak Convergence and Empirical Processes1.00094100%
2Andrews, D. and Cheng, X (2012) Estimation and inference with weak, semi-strong, and strong identification0.87452100%
3Cox, G (2022) Weak identification with bounds in a class of minimum distance models self0.87452100%
4Bai, J (1997) Estimation of a change point in multiple regression models0.67815247%
5Aubin, J.-P. and Frankowska, H (1990) Set-Valued Analysis0.6444250%
6Cox, G (2020) Almost sure uniqueness of a global minimum without convexity self0.6444250%
7Silvapulle, M. and Sen, P (2005) Constrained Statistical Inference: Inequality, Order and Shape Restrictions0.58531100%
8Stock, J. and Wright, J (2000) GMM with weak identification0.58531100%
9Andrews, D (1999) Estimation when a parameter is on a boundary0.51121100%
10Casini, A. and Perron, P (2021) Continuous record asymptotics for change-points models0.51121100%

Showing the top 10 of 44 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Weak Identification with Bounds in a Class of Minimum Distance Models0.73732