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Asymptotic analysis of the Forward Search

Author

Listed:
  • Bent Nielsen

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

  • Søren Johansen

    (Dept of Economics, University of Copenhagen and CREATES, Department of Economics and Business, Aarhus University)

Abstract

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

  • Bent Nielsen & Søren Johansen, 2013. "Asymptotic analysis of the Forward Search," Economics Papers 2013-W02, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1302
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    References listed on IDEAS

    as
    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, April.
    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. Shorack, Galen R., 1979. "Weak convergence of empirical and quantile processes in sup-norm metrics via kmt-constructions," Stochastic Processes and their Applications, Elsevier, vol. 9(1), pages 95-98, August.
    4. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," Discussion Papers 11-29, University of Copenhagen. Department of Economics.
    5. Castle, Jennifer & Shephard, Neil (ed.), 2009. "The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry," OUP Catalogue, Oxford University Press, number 9780199237197.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    2. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    3. Søren Johansen & Bent Nielsen, 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator," Econometrics, MDPI, vol. 1(1), pages 1-18, May.
    4. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    5. Petropoulou, Maria & Salanti, Georgia & Rücker, Gerta & Schwarzer, Guido & Moustaki, Irini & Mavridis, Dimitris, 2021. "A forward search algorithm for detecting extreme study effects in network meta-analysis," LSE Research Online Documents on Economics 110954, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Fixed point result; Forward Search; quantile process; weighted and marked empirical process.;
    All these keywords.

    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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