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Almost Sure Uniqueness of a Global Minimum Without Convexity

Gregory Cox

arXiv 6 Mar 2018 · Econometrics

arXiv:1803.02415 · PDF · Extracted main text

Abstract

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.

Citation extraction

48
references
60
in-text mentions
48
distinct cited
1
self-citations
7,119
main-text words

appendix boundary found by appendix_command · 54% 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
1Mallik, A., Banerjee, M., and Sen, B (2013) Asymptotics for p-value based trheshold estimation in regression settings0.87452100%
2Cox, G (2019) Weak identification with bounds in a class of minimum distance models self0.64441100%
3Guillemin, V. and Pollack, A (1974) Differential Topology0.5112250%
4Andrews, D. and Cheng, X (2012) Estimation and inference with weak, semi-strong, and strong identification0.51121100%
5Cheng, X (2015) Robust inference in nonlinear models with mixed identification strength0.51121100%
6Kim, J. and Pollard, D (1990) Cube root asymptotics0.51121100%
7Lindsay, B (1983) The geometry of mixture likelihoods: A general theory0.51121100%
8Arcones, M (1992) On the arg max of a Gaussian process0.40511100%
9Cheng, K. and Chen, C (1988) Estimation of the weibull parameters with grouped data0.40511100%
10Copas, J (1975) On the unimodality of the likelihood for the cauchy distribution0.40511100%

Showing the top 10 of 48 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
1A Generalized Argmax Theorem with Applications0.64442
2Weak Identification with Bounds in a Class of Minimum Distance Models0.40511