摘要翻译：
在排队论、空间统计学、地质统计学和气象学等许多领域中，数据是在不规则的空间位置上观测的。这种情况的一个模型包括考虑由泊松过程产生的观测点。在此假设下，我们研究了标记点过程$\{(t_i,X(t_i))\}$的部分和的极限性质，其中X(t)是平稳随机场，点t_i是由$\MathBB{R}^d$上的独立泊松随机测度$\MathBB{N}$生成的。定义了样本均值和样本方差统计量，并确定了它们在重尾条件下的联合渐近性态，从而推广了Karr[Adv.in appl.probab.18(1986)406--422]的一些有限方差结果。在重尾度未知的情况下，利用对未知均值建立置信区间的方法，给出了标记点过程中二次抽样的新结果。
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英文标题：
《Stable marked point processes》
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作者：
Tucker McElroy, Dimitris N. Politis
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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：
  In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson process. Under this assumption, we study the limit behavior of the partial sums of the marked point process $\{(t_i,X(t_i))\}$, where X(t) is a stationary random field and the points t_i are generated from an independent Poisson random measure $\mathbb{N}$ on $\mathbb{R}^d$. We define the sample mean and sample variance statistics and determine their joint asymptotic behavior in a heavy-tailed setting, thus extending some finite variance results of Karr [Adv. in Appl. Probab. 18 (1986) 406--422]. New results on subsampling in the context of a marked point process are also presented, with the application of forming a confidence interval for the unknown mean under an unknown degree of heavy tails.
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PDF链接：
https://arxiv.org/pdf/708.0536