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February 2015 Consistency of maximum likelihood estimation for some dynamical systems
Kevin McGoff, Sayan Mukherjee, Andrew Nobel, Natesh Pillai
Ann. Statist. 43(1): 1-29 (February 2015). DOI: 10.1214/14-AOS1259


We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.


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Kevin McGoff. Sayan Mukherjee. Andrew Nobel. Natesh Pillai. "Consistency of maximum likelihood estimation for some dynamical systems." Ann. Statist. 43 (1) 1 - 29, February 2015.


Published: February 2015
First available in Project Euclid: 18 November 2014

zbMATH: 1319.37006
MathSciNet: MR3285598
Digital Object Identifier: 10.1214/14-AOS1259

Primary: 37A25, 37A50, 62B10, 62F12, 62M09
Secondary: 37D20, 60F10, 62M05, 62M10, 94A17

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 1 • February 2015
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