Almost Sure Uniqueness of a Global Minimum Without Convexity

Gregory Cox

Papers from arXiv.org

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.

Date: 2018-03, Revised 2019-02
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1803.02415

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