arXiv 6 Mar 2018 · Econometrics
arXiv:1803.02415 · PDF · Extracted main text
This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.
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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 | Mallik, A., Banerjee, M., and Sen, B (2013) Asymptotics for p-value based trheshold estimation in regression settings | 0.874 | 5 | 2 | 100% |
| 2 | Cox, G (2019) Weak identification with bounds in a class of minimum distance models self | 0.644 | 4 | 1 | 100% |
| 3 | Guillemin, V. and Pollack, A (1974) Differential Topology | 0.511 | 2 | 2 | 50% |
| 4 | Andrews, D. and Cheng, X (2012) Estimation and inference with weak, semi-strong, and strong identification | 0.511 | 2 | 1 | 100% |
| 5 | Cheng, X (2015) Robust inference in nonlinear models with mixed identification strength | 0.511 | 2 | 1 | 100% |
| 6 | Kim, J. and Pollard, D (1990) Cube root asymptotics | 0.511 | 2 | 1 | 100% |
| 7 | Lindsay, B (1983) The geometry of mixture likelihoods: A general theory | 0.511 | 2 | 1 | 100% |
| 8 | Arcones, M (1992) On the arg max of a Gaussian process | 0.405 | 1 | 1 | 100% |
| 9 | Cheng, K. and Chen, C (1988) Estimation of the weibull parameters with grouped data | 0.405 | 1 | 1 | 100% |
| 10 | Copas, J (1975) On the unimodality of the likelihood for the cauchy distribution | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 48 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Generalized Argmax Theorem with Applications | 0.644 | 4 | 2 |
| 2 | Weak Identification with Bounds in a Class of Minimum Distance Models | 0.405 | 1 | 1 |