ASYMPTOTICS OF MAXIMUM-LIKELIHOOD ESTIMATORS FOR THE CURIE-WEISS MODEL

• 成果类型: Article
• 署名作者: COMETS, F; GIDAS, B
• 署名单位: Brown University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348111
• 发表日期: 1991
• 页码: 557-578
• 关键词: independent random vectors; laplace approximations; sums

摘要

We study the asymptotics of the ML estimators for the Curie-Weiss model parameterized 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 h triple-over-dot 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 n3/4h triple-over-dot n has a non-Gaussian limiting law. Away from phase transition points, h triple-over-dot n is asymptotically normal and efficient. We also study the asymptotics of the ML estimator of beta-for known h.