Moment convergence of Z-estimators

Ilia Negri; Yoichi Nishiyama

doi:10.1007/s11203-016-9146-0

Moment convergence of Z-estimators

Ilia Negri^*, Yoichi Nishiyama

^*Corresponding author for this work

School of International Liberal Studies

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	387-397
Number of pages	11
Journal	Statistical Inference for Stochastic Processes
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s11203-016-9146-0
Publication status	Published - 2017 Oct 1

Keywords

Asymptotic distribution
Cox regression
Method of moment estimators

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s11203-016-9146-0

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title = "Moment convergence of Z-estimators",

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{\textquoteright}s regression model as well as some diffusion process are discussed.",

keywords = "Asymptotic distribution, Cox regression, Method of moment estimators",

author = "Ilia Negri and Yoichi Nishiyama",

note = "Funding Information: The authors thank an anonymous referee for her or his helpful comments. This work was supported by Italian MIUR, Grant 2009 (I.N.) and by Grant-in-Aid for Scientific Research (C), 24540152, from Japan Society for the Promotion of Science (Y.N.). Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media Dordrecht.",

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doi = "10.1007/s11203-016-9146-0",

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AU - Negri, Ilia

AU - Nishiyama, Yoichi

N1 - Funding Information: The authors thank an anonymous referee for her or his helpful comments. This work was supported by Italian MIUR, Grant 2009 (I.N.) and by Grant-in-Aid for Scientific Research (C), 24540152, from Japan Society for the Promotion of Science (Y.N.). Publisher Copyright: © 2016, Springer Science+Business Media Dordrecht.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Asymptotic distribution

KW - Cox regression

KW - Method of moment estimators

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Moment convergence of Z-estimators

Abstract

Keywords

ASJC Scopus subject areas

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