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Moment convergence of Z-estimators

Author

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  • Ilia Negri

    (University of Bergamo)

  • Yoichi Nishiyama

    (Waseda University)

Abstract

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.

Suggested Citation

  • Ilia Negri & Yoichi Nishiyama, 2017. "Moment convergence of Z-estimators," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 387-397, October.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-016-9146-0
    DOI: 10.1007/s11203-016-9146-0
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
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    Cited by:

    1. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.

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