2010 Fiscal Year Final Research Report

Statistical inference for inhomogeneous spatial Markov point processes

Research Project

Project/Area Number	21700319
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	Statistical science
Research Institution	Oita University of Nursing and Health Sciences
Principal Investigator	SAKAGUCHI Takayuki Oita University of Nursing and Health Sciences, 看護学部, 助教 (10436496)
Project Period (FY)	2009 – 2010
Keywords	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
Research Abstract	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.