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Acta scientiarum naturalium Universitatis Pekinensis

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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

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