Statistical inference for inhomogeneous spatial Markov point processes

非齐次空间马尔可夫点过程的统计推断

• 批准号: 21700319
• 负责人: SAKAGUCHI Takayuki
• 金额: $ 1.58万
• 依托单位: Oita University of Nursing and Health Sciences
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21700319/
• 关键词: 非定常マルコフ空間点過程; TIMモデル; 最尤推定; 一致性; 漸近正規性; エルゴード性; エルゴード定理

In this research, we focused on TIM models for spatial point processes and studied asymptotic behavior of maximum likelihood estimators for model parameters. The purpose of this study is to investigate under which conditions consistency and asymptotic normality of the maximum likelihood estimators are assured. Ergodic theorems and central limit theorems for homogeneous spatial processes are keys for our problems. But these theorems cannot be applied directly. Therefore we discussed the applicability of the theorems. Unfortunately we failed to give precise conditions and further research will be needed.

在这项研究中，我们专注于用于空间点过程的TIM模型，并研究了模型参数的最大似然估计器的渐近行为。这项研究的目的是在确保最大似然估计剂的条件一致性和渐近正态性下进行研究。均质空间过程的奇异定理和中央限制定理是我们问题的关键。但是这些定理不能直接应用。因此，我们讨论了定理的适用性。不幸的是，我们未能提供精确的条件，需要进一步研究。