Asymptotic Properties of Maximum Likelihood Estimation: Parameterized Diffusion in a Manifold

被引:0
作者
Said, S. [1 ]
Manton, J. H. [1 ]
机构
[1] Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic 3010, Australia
关键词
Asymptotic normality; Differentiable manifold; Elliptic diffusion; Fisher information; Maximum likelihood; SIGNAL-DETECTION;
D O I
10.1080/07362994.2013.865539
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.
引用
收藏
页码:298 / 327
页数:30
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