Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case,Annals of the Institute of Statistical Mathematics

当前位置： X-MOL 学术 › Ann. Inst. Stat. Math. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case
Annals of the Institute of Statistical Mathematics ( IF 0.8 ) Pub Date : 2021-01-01 , DOI: 10.1007/s10463-020-00775-y
Federico Camerlenghi , Claudio Macci , Elena Villa

The mean density estimation of a random closed set in $$\mathbb {R}^d$$ R d , based on a single observation, is a crucial problem in several application areas. In the case of stationary random sets, a common practice to estimate the mean density is to take the n -dimensional volume fraction with observation window as large as possible. In the present paper, we provide large and moderate deviation results for these estimators when the random closed set $$\Theta _n$$ Θ n belongs to the quite general class of stationary Boolean models with Hausdorff dimension $$n

中文翻译：

基于单个观察的平均密度估计器的渐近行为：布尔模型案例

$$\mathbb {R}^d$$ R d 中随机闭集的平均密度估计，基于单个观察，是几个应用领域的关键问题。在平稳随机集的情况下，估计平均密度的常见做法是取观察窗口尽可能大的 n 维体积分数。在本文中，当随机闭集 $$\Theta _n$$ Θ n 属于具有 Hausdorff 维数 $$n 的平稳布尔模型的相当一般类别时，我们为这些估计量提供了大和中等偏差结果

更新日期：2021-01-01

点击分享查看原文

点击收藏

阅读更多本刊最新论文本刊介绍/投稿指南11