On the Convergence of Monte Carlo Maximum Likelihood Calculations
On the Convergence of Monte Carlo Maximum Likelihood Calculations
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DOI：
10.1111/j.2517-6161.1994.tb01976.x
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
C. Geyer
中科院分区：
文献类型：
--
作者：
C. Geyer
摘要：归一化分布族的蒙特卡罗最大似然法可用于非常广泛的一类模型。考虑到任何家庭{他：0 E 0 }的非负可积函数，通过将函数归一化为积分为1得到的族中的最大似然估计可以通过Monte Carlo模拟来近似，唯一的正则性条件是参数空间的紧化，使得评估图0 h 0（x）保持连续。然后，概率为1的Monte Carlo近似的对数似然hypoconvergence的确切的对数似然，其最大化收敛到确切的最大似然估计，近似的轮廓似然hypoconvergence的确切的轮廓和水平集的近似似然（支持区域）收敛到确切的集合（在Painleve-Kuratowski集收敛）。当有缺失数据时，如果Wald型可积性条件得到满足，同样的结果也成立。渐近正态性的Monte Carlo误差和收敛的Monte Carlo近似所观察到的Fisher信息。
SUMMARY Monte Carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models. Given any family { he: 0 E 0 } of non-negative integrable functions, maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by Monte Carlo simulation, the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0(x) remain continuous. Then with probability 1 the Monte Carlo approximant to the log-likelihood hypoconverges to the exact log-likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painleve-Kuratowski set convergence). The same results hold when there are missing data if a Wald-type integrability condition is satisfied. Asymptotic normality of the Monte Carlo error and convergence of the Monte Carlo approximation to the observed Fisher information are also shown.