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.

在本研究中，我们重点关注空间点过程的 TIM 模型，并研究模型参数的最大似然估计量的渐近行为。本研究的目的是研究在什么条件下可以保证最大似然估计量的一致性和渐近正态性。齐次空间过程的遍历定理和中心极限定理是我们问题的关键。但这些定理不能直接应用。因此我们讨论了定理的适用性。不幸的是我们未能给出精确的条件，需要进一步的研究。