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February 2020 Almost sure uniqueness of a global minimum without convexity
Gregory Cox
Ann. Statist. 48(1): 584-606 (February 2020). DOI: 10.1214/19-AOS1829

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. "Almost sure uniqueness of a global minimum without convexity." Ann. Statist. 48 (1) 584 - 606, February 2020. https://doi.org/10.1214/19-AOS1829

Information

Received: 1 May 2018; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196552
MathSciNet: MR4065175
Digital Object Identifier: 10.1214/19-AOS1829

Subjects:
Primary: 60G17

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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