摘要翻译:
本文讨论了当混合分量对称且来自同一位置族时,有限混合的参数估计问题。我们把这些混合称为半参数,因为除了对称性之外,没有关于分量分布的参数形式的额外假设。由于对称分布的类别是如此广泛,参数的可辨识性是这些混合中的一个主要问题。我们提出了有限混合模型的可辨识性的概念,我们称之为k-可辨识性,其中k表示混合模型中组分的个数。给出了当k=2或3时对称分量位置混合的k-可辨识性的充分条件。提出了一种新的基于距离的K-可辨识模型的位置和混合参数估计方法,并证明了估计量的强相合性和渐近正态性。在L2距离的具体情况下,我们证明了我们的估计推广了Hodges-Lehmann估计。我们讨论了这些过程的数值实现,以及在两分量情况下分量分布的经验估计。与假设正态分量的最大似然估计相比,在分量确实正态的情况下,我们的方法产生了较高的标准误差估计,但当分量是重尾的情况下,我们的方法显著优于正态方法。
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英文标题:
《Inference for mixtures of symmetric distributions》
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作者:
David R. Hunter, Shaoli Wang, Thomas P. Hettmansperger
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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:
This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the component distributions. Because the class of symmetric distributions is so broad, identifiability of parameters is a major issue in these mixtures. We develop a notion of identifiability of finite mixture models, which we call k-identifiability, where k denotes the number of components in the mixture. We give sufficient conditions for k-identifiability of location mixtures of symmetric components when k=2 or 3. We propose a novel distance-based method for estimating the (location and mixing) parameters from a k-identifiable model and establish the strong consistency and asymptotic normality of the estimator. In the specific case of L_2-distance, we show that our estimator generalizes the Hodges--Lehmann estimator. We discuss the numerical implementation of these procedures, along with an empirical estimate of the component distribution, in the two-component case. In comparisons with maximum likelihood estimation assuming normal components, our method produces somewhat higher standard error estimates in the case where the components are truly normal, but dramatically outperforms the normal method when the components are heavy-tailed.
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PDF链接:
https://arxiv.org/pdf/708.0499