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2018 Consistency of logistic classifier in abstract Hilbert spaces
Agne Kazakeviciute, Malini Olivo
Electron. J. Statist. 12(2): 4487-4516 (2018). DOI: 10.1214/18-EJS1514

Abstract

We study the asymptotic behavior of the logistic classifier in an abstract Hilbert space and require realistic conditions on the distribution of data for its consistency. The number $k_{n}$ of estimated parameters via maximum quasi-likelihood is allowed to diverge so that $k_{n}/n\to 0$ and $n\tau_{k_{n}}^{4}\to\infty$, where $n$ is the number of observations and $\tau_{k_{n}}$ is the variance of the last principal component of data used for estimation. This is the only result on the consistency of the logistic classifier we know so far when the data are assumed to come from a Hilbert space.

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Agne Kazakeviciute. Malini Olivo. "Consistency of logistic classifier in abstract Hilbert spaces." Electron. J. Statist. 12 (2) 4487 - 4516, 2018. https://doi.org/10.1214/18-EJS1514

Information

Received: 1 May 2018; Published: 2018
First available in Project Euclid: 19 December 2018

zbMATH: 07003249
MathSciNet: MR3892702
Digital Object Identifier: 10.1214/18-EJS1514

Keywords: ‎classification‎ , consistency , Functional data analysis , logistic classifier

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Vol.12 • No. 2 • 2018
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