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Asymptotic analysis of the Forward Search


  • Søren Johansen

    () (University of Copenhagen and CREATES)

  • Bent Nielsen

    () (Nuffield College & Department of Economics, University of Oxford & Institute for New Economic Thinking at the Oxford Martin School.)


The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made. The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure.

Suggested Citation

  • Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," CREATES Research Papers 2013-05, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2013-05

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    References listed on IDEAS

    1. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466.
    2. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, July.
    3. Bent Nielsen & Soren Johansen, 2010. "Discussion of The Forward Search: Theory and Data Analysis," Economics Series Working Papers 2010-W02, University of Oxford, Department of Economics.
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    More about this item


    Fixed point result; Forward Search; quantile process; weighted and marked empirical process;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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