Open Access
Translator Disclaimer
June, 1991 Asymptotics of Maximum Likelihood Estimators for the Curie-Weiss Model
Francis Comets, Basilis Gidas
Ann. Statist. 19(2): 557-578 (June, 1991). DOI: 10.1214/aos/1176348111


We study the asymptotics of the ML estimators for the Curie-Weiss model parametrized by the inverse temperature $\beta$ and the external field $h$. We show that if both $\beta$ and $h$ are unknown, the ML estimator of $(\beta, h)$ does not exist. For $\beta$ known, the ML estimator $\hat{h}_n$ of $h$ exhibits, at a first order phase transition point, superefficiency in the sense that its asymptotic variance is half of that of nearby points. At the critical point $(\beta = 1)$, if the true value is $h = 0$, then $n^{3/4}\hat h_n$ has a non-Gaussian limiting law. Away from phase transition points, $\hat h_n$ is asymptotically normal and efficient. We also study the asymptotics of the ML estimator of $\beta$ for known $h$.


Download Citation

Francis Comets. Basilis Gidas. "Asymptotics of Maximum Likelihood Estimators for the Curie-Weiss Model." Ann. Statist. 19 (2) 557 - 578, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0749.62018
MathSciNet: MR1105836
Digital Object Identifier: 10.1214/aos/1176348111

Primary: 62F10
Secondary: 62F12 , 62F99 , 62P99

Keywords: asymptotic normality , consistency , maximum likelihood estimators , Phase transitions , superefficiency

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
Back to Top