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2020 The existence of maximum likelihood estimate in high-dimensional binary response generalized linear models
Wenpin Tang, Yuting Ye
Electron. J. Statist. 14(2): 4028-4053 (2020). DOI: 10.1214/20-EJS1766

Abstract

Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and elliptical covariates. This extends a previous result of Candès and Sur who proved the phase transition for the logistic regression with Gaussian covariates. Our result reveals a rich structure in the phase transition phenomenon, which is simply overlooked by Gaussianity. The main tools for deriving the result are data separation, convex geometry and stochastic approximation. We also conduct simulation studies to corroborate our theoretical findings, and explore other features of the problem.

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Wenpin Tang. Yuting Ye. "The existence of maximum likelihood estimate in high-dimensional binary response generalized linear models." Electron. J. Statist. 14 (2) 4028 - 4053, 2020. https://doi.org/10.1214/20-EJS1766

Information

Received: 1 April 2020; Published: 2020
First available in Project Euclid: 30 October 2020

zbMATH: 07270285
MathSciNet: MR4168791
Digital Object Identifier: 10.1214/20-EJS1766

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Vol.14 • No. 2 • 2020
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