摘要翻译:
假设我们观察到一个几何遍历的半马尔可夫过程,并对嵌入马尔可夫链的转移分布、到达间时间的条件分布或两者都有一个参数模型。前两个模型是半参数的,参数可以用条件极大似然估计来估计。过程的第三个模型是参数的,参数可以用无条件极大似然估计器估计。我们启发式地确定了这些估计量的渐近分布,并证明了它们是渐近有效的。如果参数模型不正确,则(条件)极大似然估计器估计使Kullback-Leibler信息最大化的参数。我们证明了它们在非参数意义下保持渐近有效。
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英文标题:
《Optimality of estimators for misspecified semi-Markov models》
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作者:
Ursula U. M\"uller, Anton Schick, Wolfgang Wefelmeyer
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two models for the process are semiparametric, and the parameters can be estimated by conditional maximum likelihood estimators. The third model for the process is parametric, and the parameter can be estimated by an unconditional maximum likelihood estimator. We determine heuristically the asymptotic distributions of these estimators and show that they are asymptotically efficient. If the parametric models are not correct, the (conditional) maximum likelihood estimators estimate the parameter that maximizes the Kullback--Leibler information. We show that they remain asymptotically efficient in a nonparametric sense.
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PDF链接:
https://arxiv.org/pdf/712.3451