Nonparametric inference in multiplicative intensity model by discrete time observation

Yoichi Nishiyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper deals with nonparametric inference problems in the multiplicative intensity model for counting processes. We propose a Nelson-Aalen type estimator based on discrete observation. The functional asymptotic normality of the estimator is proved. The limit process is the same as that in the continuous observation case, thus the proposed estimator based on discrete observation has the same properties as the Nelson-Aalen estimator based on continuous observation. For example, the asymptotic efficiency of proposed estimator is valid based on less information than the continuous observation case. A Kaplan-Meier type estimator is also discussed. Nonparametric goodness of fit test is considered, and an asymptotically distribution free test is proposed.

Original languageEnglish
Pages (from-to)823-833
Number of pages11
JournalAnnals of the Institute of Statistical Mathematics
Issue number5
Publication statusPublished - 2010 Oct
Externally publishedYes


  • Counting process
  • Discrete observation
  • Multiplicative intensity model
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability


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