IDEAS home Printed from https://ideas.repec.org/p/nuf/econwp/1904.html
   My bibliography  Save this paper

Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

Author

Listed:
  • Vanessa Berenguer-Rico

    (Department of Economics and Mansfield College, University of Oxford)

  • Søren Johansen

    (University of Copenhagen and CREATES and Aarhus University)

  • Bent Nielsen

    (Department of Economics and Nuffield College, University of Oxford)

Abstract

A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker su¢ cient conditions for uniform consistency are derived. The theory allows for a wide variety of regressors and error distributions. We apply the theory to 1-step Huber-skip estimators. These estimators describe the widespread practice of removing outlying observations from an intial estimation of the model of interest and updating the estimation in a second step by applying least squares to the selected observations. Two results are presented. First, we give new and weaker conditions for consistency of the estimators. Second, we analyze the gauge, which is the rate of false detection of outliers, and which can be used to decide the cut-o§ in the rule for selecting outliers.

Suggested Citation

  • Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals," Economics Papers 2019-W04, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1904
    as

    Download full text from publisher

    File URL: https://www.nuffield.ox.ac.uk/economics/Papers/2019/2019W04_EP_VSB_consis_24may2019.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
    2. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    3. David Hendry & Carlos Santos, 2010. "An Automatic Test of Super Exogeneity," Economics Series Working Papers 476, University of Oxford, Department of Economics.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Søren Johansen & Bent Nielsen, 2016. "Rejoinder: Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 374-381, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood," CREATES Research Papers 2019-15, Department of Economics and Business Economics, Aarhus University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiyu Jiao & Felix Pretis, 2022. "Testing the Presence of Outliers in Regression Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(6), pages 1452-1484, December.
    2. Ericsson, Neil R., 2016. "Eliciting GDP forecasts from the FOMC’s minutes around the financial crisis," International Journal of Forecasting, Elsevier, vol. 32(2), pages 571-583.
    3. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    4. Jiao, Xiyu & Pretis, Felix & Schwarz, Moritz, 2024. "Testing for coefficient distortion due to outliers with an application to the economic impacts of climate change," Journal of Econometrics, Elsevier, vol. 239(1).
    5. Andrew B. Martinez, 2020. "Forecast Accuracy Matters for Hurricane Damage," Econometrics, MDPI, vol. 8(2), pages 1-24, May.
    6. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2023. "Robust Discovery of Regression Models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 31-51.
    7. Ericsson, Neil R., 2017. "How biased are U.S. government forecasts of the federal debt?," International Journal of Forecasting, Elsevier, vol. 33(2), pages 543-559.
    8. Hendry, David F., 2018. "Deciding between alternative approaches in macroeconomics," International Journal of Forecasting, Elsevier, vol. 34(1), pages 119-135.
    9. Ericsson, Neil R., 2017. "Interpreting estimates of forecast bias," International Journal of Forecasting, Elsevier, vol. 33(2), pages 563-568.
    10. Jennifer L. Castle & David F. Hendry & Andrew B. Martinez, 2017. "Evaluating Forecasts, Narratives and Policy Using a Test of Invariance," Econometrics, MDPI, vol. 5(3), pages 1-27, September.
    11. Andrew B. Martinez & Neil R. Ericsson, 2025. "Improving empirical models and forecasts with saturation-based machine learning," Annals of Operations Research, Springer, vol. 346(1), pages 447-487, March.
    12. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    13. David F. Hendry, 2024. "A Brief History of General‐to‐specific Modelling," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 1-20, February.
    14. Jennifer Castle & David Hendry, 2016. "Policy Analysis, Forediction, and Forecast Failure," Economics Series Working Papers 809, University of Oxford, Department of Economics.
    15. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    16. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
    17. Baiardi, Donatella & Morana, Claudio, 2021. "Climate change awareness: Empirical evidence for the European Union," Energy Economics, Elsevier, vol. 96(C).
    18. David H. Bernstein & Andrew B. Martinez, 2021. "Jointly Modeling Male and Female Labor Participation and Unemployment," Econometrics, MDPI, vol. 9(4), pages 1-14, December.
    19. Emmanuel Flachaire & Sullivan Hué & Sébastien Laurent & Gilles Hacheme, 2024. "Interpretable Machine Learning Using Partial Linear Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 519-540, June.
    20. Anthony C. Atkinson & Andrea Cerioli & Marco Riani, 2016. "Discussion of ‘Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models’ by Johansen and Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 349-352, June.

    More about this item

    Keywords

    1-step Huber skip; Asymptotic theory; Empirical processes; Gauge; Marked and Weighted Empirical processes; Non-stationarity; Robust Statistics; Stationarity;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nuf:econwp:1904. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Maxine Collett (email available below). General contact details of provider: https://www.nuffield.ox.ac.uk/economics/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.