Z-estimators and auxiliary information for strong mixing processes

  • Federico CruduEmail author
  • Emilio Porcu
Original Paper


This paper introduces a weighted Z-estimator for moment condition models, assuming auxiliary information on the unknown distribution of the data and under the assumption of weak dependence (strong mixing processes). We model serial dependence through a simple nonparametric blocking device, routinely used in the bootstrap literature. The weights that carry the auxiliary information are computed by means of generalized empirical likelihood. The resulting weighted estimator is shown to be consistent and asymptotically normal. The proposed estimator is computationally simple and shows nice finite sample features when compared to asymptotically equivalent estimators.


Z-estimators M-estimators GMM Generalized empirical likelihood Blocking techniques \(\alpha\)-Mixing 



Federico Crudu’s research is supported by Proyecto Fondecyt Iniciacion N. 11140433 from the Chilean Government. Research work of Emilio Porcu is supported by Proyecto Fondecyt Regular N. 1170290 from the Chilean Government.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics and StatisticsUniversity of SienaSienaItaly
  2. 2.School of Mathematics, Statistics and PhysicsNewcastle UniversityNewcastle upon TyneUK
  3. 3.Centre for North South Economic ResearchUniversity of CagliariCagliariItaly
  4. 4.Departamento de MatemáticasUniversidad de AtacamaCopiapóChile

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