摘要翻译:
本文在两种情况下研究了双参数$(\alpha,\theta)$Poisson-Dirichlet过程的大样本性质。在估计未知概率测度的贝叶斯背景下,将此过程看作Dirichlet过程的自然推广,研究了两参数Poisson-Dirichlet后验过程的相合性和弱收敛性。我们还建立了两参数Poisson-Dirichlet过程对大$θ+nα的弱收敛性,这一结果补充了Dirichlet过程和Poisson-Dirichlet序列的大$θ结果,并补充了关于两参数Poisson-Dirichlet过程大偏差原理的最新结果。我们的结果的一个关键组成部分是使用分布标识,这在其他上下文中可能很有用。
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英文标题:
《Large sample asymptotics for the two-parameter Poisson--Dirichlet
process》
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作者:
Lancelot F. James
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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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 paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension of the Dirichlet process, we explore the consistency and weak convergence of the the two-parameter Poisson--Dirichlet posterior process. We also establish the weak convergence of properly centered two-parameter Poisson--Dirichlet processes for large $\theta+n\alpha.$ This latter result complements large $\theta$ results for the Dirichlet process and Poisson--Dirichlet sequences, and complements a recent result on large deviation principles for the two-parameter Poisson--Dirichlet process. A crucial component of our results is the use of distributional identities that may be useful in other contexts.
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PDF链接:
https://arxiv.org/pdf/708.4294