IDEAS home Printed from https://ideas.repec.org/p/aah/create/2019-12.html
   My bibliography  Save this paper

Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

Author

Listed:
  • Vanessa Berenguer-Rico

    (University of Oxford)

  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Bent Nielsen

    (University of Oxford)

Abstract

A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker sufficient 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-off 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," CREATES Research Papers 2019-12, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2019-12
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/19/rp19_12.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. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. 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.
    4. David Hendry & Carlos Santos, 2010. "An Automatic Test of Super Exogeneity," Economics Series Working Papers 476, University of Oxford, Department of Economics.
    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. Hendry, David F., 2018. "Deciding between alternative approaches in macroeconomics," International Journal of Forecasting, Elsevier, vol. 34(1), pages 119-135.
    6. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    7. Andrew B. Martinez, 2020. "Forecast Accuracy Matters for Hurricane Damage," Econometrics, MDPI, vol. 8(2), pages 1-24, May.
    8. 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.
    9. 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.
    10. Jennifer Castle & David Hendry, 2016. "Policy Analysis, Forediction, and Forecast Failure," Economics Series Working Papers 809, University of Oxford, Department of Economics.
    11. Ericsson, Neil R., 2017. "Interpreting estimates of forecast bias," International Journal of Forecasting, Elsevier, vol. 33(2), pages 563-568.
    12. 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.
    13. 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.).
    14. Pretis, Felix, 2020. "Econometric modelling of climate systems: The equivalence of energy balance models and cointegrated vector autoregressions," Journal of Econometrics, Elsevier, vol. 214(1), pages 256-273.
    15. Baiardi, Donatella & Morana, Claudio, 2021. "Climate change awareness: Empirical evidence for the European Union," Energy Economics, Elsevier, vol. 96(C).
    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. Sullivan Hué, 2022. "GAM(L)A: An econometric model for interpretable machine learning," French Stata Users' Group Meetings 2022 19, Stata Users Group.
    18. Corbellini, Aldo & Magnani, Marco & Morelli, Gianluca, 2021. "Labor market analysis through transformations and robust multivariate models," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    19. Felix Pretis & Lea Schneider & Jason E. Smerdon & David F. Hendry, 2016. "Detecting Volcanic Eruptions In Temperature Reconstructions By Designed Break-Indicator Saturation," Journal of Economic Surveys, Wiley Blackwell, vol. 30(3), pages 403-429, July.
    20. Atkinson, Anthony C. & Riani, Marco & Torti, Francesca, 2016. "Robust methods for heteroskedastic regression," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 209-222.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aah:create:2019-12. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.