摘要翻译:
本文研究了密度估计实验与Poisson实验在Le Cam意义下的渐近等价性。渐近等价性的意义在于,所有渐近最优的统计过程都可以从一个实验转移到另一个实验。这里给出的等价性是在参数空间$\mathcal{F}$上的一个弱假设下建立的。特别地,在$\mathcal{F}$上给出了一个尖锐的Besov光滑性条件,即如果$\mathcal{F}$在Besov球$B_{p,q}^{\alpha}(M)$中,且$\alpha p>1/2$。例子表明,当$\alpha p<1/2$时,中毒是不可能的。此外,对于所有紧致子集C([0,1]^m)$建立了密度估计模型及其Poisson实验的渐近等价性,该条件包括光滑度$alpha>0$的所有H“{o}lder球。
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英文标题:
《A complement to Le Cam's theorem》
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作者:
Mark G. Low, Harrison H. Zhou
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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 paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space $\mathcal{F}$. In particular, a sharp Besov smoothness condition is given on $\mathcal{F}$ which is sufficient for Poissonization, namely, if $\mathcal{F}$ is in a Besov ball $B_{p,q}^{\alpha}(M)$ with $\alpha p>1/2$. Examples show Poissonization is not possible whenever $\alpha p<1/2$. In addition, asymptotic equivalence of the density estimation model and the accompanying Poisson experiment is established for all compact subsets of $C([0,1]^m)$, a condition which includes all H\"{o}lder balls with smoothness $\alpha>0$.
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PDF链接:
https://arxiv.org/pdf/708.2233