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VOL. 77 | 2018 The multiple roots phenomenon in maximum likelihood estimation for factor analysis
Elizabeth Gross, Sonja Petrović, Donald Richards, Despina Stasi

Editor(s) Takayuki Hibi

Abstract

Multiple root estimation problems in statistical inference arise in many contexts in the literature. In maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum likelihood estimators using hill-climbing algorithms, and consequent difficulties in the resulting statistical inference.

In this paper, we study the multiple roots phenomenon in maximum likelihood estimation for factor analysis. We prove that the corresponding likelihood equations have uncountably many feasible solutions even in the simplest cases. For the case in which the observed data are two-dimensional and the unobserved factor scores are one-dimensional, we prove that the solutions to the likelihood equations form a one-dimensional real curve.

Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07034250
MathSciNet: MR3839707

Digital Object Identifier: 10.2969/aspm/07710109

Subjects:
Primary: 62F10, 62F30, 62H12, 62H20, 62H25, 62N02

Rights: Copyright © 2018 Mathematical Society of Japan

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