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Almost Sure Uniqueness of a Global Minimum Without Convexity

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  • Gregory Cox

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. "Almost Sure Uniqueness of a Global Minimum Without Convexity," Papers 1803.02415, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1803.02415
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    Cited by:

    1. Isaiah Andrews & Toru Kitagawa & Adam McCloskey, 2018. "Inference on winners," CeMMAP working papers CWP31/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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