Almost Sure Uniqueness of a Global Minimum Without Convexity
Econometrics
2019-02-20 v3 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1803.02415,
title = {Almost Sure Uniqueness of a Global Minimum Without Convexity},
author = {Gregory Cox},
journal= {arXiv preprint arXiv:1803.02415},
year = {2019}
}