Moment convergence of Z-estimators

Ilia Negri*, Yoichi Nishiyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.

Original languageEnglish
Pages (from-to)387-397
Number of pages11
JournalStatistical Inference for Stochastic Processes
Issue number3
Publication statusPublished - 2017 Oct 1


  • Asymptotic distribution
  • Cox regression
  • Method of moment estimators

ASJC Scopus subject areas

  • Statistics and Probability


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