Asymptotic Analysis of Iterated 1-Step Huber-Skip M-Estimators with Varying Cut-Offs

  • Xiyu JiaoEmail author
  • Bent Nielsen
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 193)


We consider outlier detection algorithms for time series regression based on iterated 1-step Huber-skip M-estimators. This paper analyses the role of varying cut-offs in such algorithms. The argument involves an asymptotic theory for a new class of weighted and marked empirical processes allowing for estimation errors of the scale and the regression coefficient.


The iterated 1-step Huber-skip M-estimator Tightness A fixed point Poisson approximation to gauge Weighted and marked empirical processes 



The second author is grateful to the Programme of Economic Modelling, which is part of Institute for New Economic Thinking at the Oxford Martin School. We thank Jana Jurečková and two anonymous referees for many constructive suggestions for improvement of the manuscript.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Oxford and Mansfield CollegeOxford OX1 3TFUK
  2. 2.Department of EconomicsUniversity of Oxford and Nuffield CollegeOxford OX1 1NFUK

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