Acta Scientiarum Naturalium Universitatis Pekinensis

    Next Articles

Law of Iterated Logarithms of MLE for Non-homogeneous Poisson Processes

FANG Xiangzhong   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1997-04-25 Online:1998-09-20 Published:1998-09-20



  1. 北京大学数学学院,北京,100871

Abstract: This paper study the law of iterated logarithms of maximum likelihood estimate for general non-homogeneous Poisson processes. Suppose{N(t), t≥0} is a Poisson process on probability space{Ω, F, Pθ}, where θ=(θ1,...,θm) is unknown parameter. Let θ=(θ1,...,θm) be the true value of θ, θ(T)=(θ1(T),...,θm(T)) be the MLE of θ and (aij)i,j=1,...,m the inverse martrix of the information matrix, then under some conditions, for any i(1≤im), the following equation hold

Key words: Poisson processes, strong consistency, law of iterated logarithm

摘要: 对于具有向量参数的非齐次泊松过程的一般模型,论证了向量参数极大似然估计每个分量的收敛速度符合重对数律。

关键词: 泊松点过程, 强相合性, 重对数律

CLC Number: