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A robust scale estimator based on the shortest half

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  • P.J. Rousseeuw
  • A.M. Leroy

Abstract

A new robust estimator of scale is considered, which is proportional to the length of the shortest half of the sample. The estimator is compared to the interquartile range and the median absolute deviation, that are also based on order statistics. All three estimators have the same influence function, but their breakdown points differ. It also turns out that one needs a finite‐sample correction factor which depends on mod(sample size, 4) to achieve approximate unbiasedness at normal distributions.

Suggested Citation

  • P.J. Rousseeuw & A.M. Leroy, 1988. "A robust scale estimator based on the shortest half," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(2), pages 103-116, June.
    • Handle: RePEc:bla:stanee:v:42:y:1988:i:2:p:103-116
    DOI: 10.1111/j.1467-9574.1988.tb01224.x
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    Cited by:

    1. Christmann, Andreas, 1998. "On group sequential tests based on robust location and scale estimators in the two-sample problem," Technical Reports 1998,02, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Jondeau, Eric & Lahaye, Jérôme & Rockinger, Michael, 2015. "Estimating the price impact of trades in a high-frequency microstructure model with jumps," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 205-224.
    3. Dewachter, Hans & Erdemlioglu, Deniz & Gnabo, Jean-Yves & Lecourt, Christelle, 2014. "The intra-day impact of communication on euro-dollar volatility and jumps," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 131-154.
    4. Fried, Roland & Gather, Ursula, 2007. "On rank tests for shift detection in time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 221-233, September.
    5. Pawlitschko, Jörg, 2001. "Robust estimation of the location parameter from a two-parameter exponential distribution," Technical Reports 2001,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Jérôme Lahaye & Christopher Neely, 2020. "The Role of Jumps in Volatility Spillovers in Foreign Exchange Markets: Meteor Shower and Heat Waves Revisited," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 410-427, April.
    7. Olive, David J., 2007. "Prediction intervals for regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3115-3122, March.
    8. A. Christmann & U. Gather & G. Scholz, 1994. "Some properties of the length of the shortest half," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 209-213, November.
    9. Fried, Roland, 2007. "On the robust detection of edges in time series filtering," Technical Reports 2007,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Erdemlioglu, Deniz & Laurent, Sébastien & Neely, Christopher J., 2015. "Which continuous-time model is most appropriate for exchange rates?," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 256-268.
    11. Leclerc J., 2000. "Strong Limiting Behavior Of Two Estimates Of The Mode : The Shorth And The Naive Estimator," Statistics & Risk Modeling, De Gruyter, vol. 18(4), pages 413-428, April.
    12. Gather, Ursula & Schultze, Verena, 1997. "Robust extimation of scale of an exponential distribution," Technical Reports 1997,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    13. Fried, Roland, 2007. "On the robust detection of edges in time series filtering," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1063-1074, October.
    14. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427, Edward Elgar Publishing.
    15. Di Bucchianico, A. & Einmahl, J.H.J. & Mushkudiani, N.A., 2001. "Smallest nonparametric tolerance regions," Other publications TiSEM 436f9be2-d0ad-49af-b6df-9, Tilburg University, School of Economics and Management.
    16. Yi, Chae-Deug, 2020. "Jump probability using volatility periodicity filters in US Dollar/Euro exchange rates," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    17. Fried, Roland H., 2003. "Robust filtering of time series with trends," Technical Reports 2003,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. Schettlinger, Karen & Fried, Roland & Gather, Ursula, 2006. "Robust Filters for Intensive Care Monitoring: Beyond the Running Median," Technical Reports 2006,23, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    19. Dumitru, Ana-Maria & Urga, Giovanni, 2016. "Jumps and Information Asymmetry in the US Treasury Market," EconStor Preprints 130148, ZBW - Leibniz Information Centre for Economics.
    20. Fried, Roland & Gather, Ursula, 2006. "On rank tests for shift detection in time series," Technical Reports 2006,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    21. Boudt, Kris & Croux, Christophe & Laurent, Sébastien, 2011. "Robust estimation of intraweek periodicity in volatility and jump detection," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 353-367, March.
    22. YI, Chae-Deug, 2023. "Exchange rate volatility and intraday jump probability with periodicity filters using a local robust variance," Finance Research Letters, Elsevier, vol. 55(PA).

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