Almost Sure Uniqueness of a Global Minimum Without Convexity

Gregory Cox

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arXiv · 1803.02415

Almost Sure Uniqueness of a Global Minimum Without Convexity

Gregory Cox

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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.

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Gregory Cox. 2018-03-06. Almost Sure Uniqueness of a Global Minimum Without Convexity. https://arxiv.org/abs/1803.02415

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