Moment convergence of Z-estimators

Ilia Negri, Yoichi Nishiyama

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1-11
Number of pages11
JournalStatistical Inference for Stochastic Processes
DOIs
Publication statusAccepted/In press - 2016 Jul 16

Fingerprint

M-estimator
Moment
Estimator
Cox Regression Model
Large Deviations
Diffusion Process
Asymptotic distribution
Rate of Convergence
Statistics
Necessary
Alternatives
Model
Range of data
Observation

Keywords

  • Asymptotic distribution
  • Cox regression
  • Method of moment estimators

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Moment convergence of Z-estimators. / Negri, Ilia; Nishiyama, Yoichi.

In: Statistical Inference for Stochastic Processes, 16.07.2016, p. 1-11.

Research output: Contribution to journalArticle

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