arXiv 19 Sep 2022 · Econometrics · 1 citations (OpenAlex)
arXiv:2209.08793 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | van der Vaart, A. and Wellner, J (1996) Weak Convergence and Empirical Processes | 1.000 | 9 | 4 | 100% |
| 2 | Andrews, D. and Cheng, X (2012) Estimation and inference with weak, semi-strong, and strong identification | 0.874 | 5 | 2 | 100% |
| 3 | Cox, G (2022) Weak identification with bounds in a class of minimum distance models self | 0.874 | 5 | 2 | 100% |
| 4 | Bai, J (1997) Estimation of a change point in multiple regression models | 0.678 | 15 | 2 | 47% |
| 5 | Aubin, J.-P. and Frankowska, H (1990) Set-Valued Analysis | 0.644 | 4 | 2 | 50% |
| 6 | Cox, G (2020) Almost sure uniqueness of a global minimum without convexity self | 0.644 | 4 | 2 | 50% |
| 7 | Silvapulle, M. and Sen, P (2005) Constrained Statistical Inference: Inequality, Order and Shape Restrictions | 0.585 | 3 | 1 | 100% |
| 8 | Stock, J. and Wright, J (2000) GMM with weak identification | 0.585 | 3 | 1 | 100% |
| 9 | Andrews, D (1999) Estimation when a parameter is on a boundary | 0.511 | 2 | 1 | 100% |
| 10 | Casini, A. and Perron, P (2021) Continuous record asymptotics for change-points models | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 44 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Weak Identification with Bounds in a Class of Minimum Distance Models | 0.737 | 3 | 2 |