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The half-half plot

Author

Listed:
  • Einmahl, J.H.J.

    (Tilburg University, School of Economics and Management)

  • Gantner, M.

    (Tilburg University, School of Economics and Management)

Abstract

The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence 1/√n . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online.
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Suggested Citation

  • Einmahl, J.H.J. & Gantner, M., 2012. "The half-half plot," Other publications TiSEM 00018d48-5993-467c-a585-9, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:00018d48-5993-467c-a585-92dcede31ef3
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/1431319/supplement_final.pdf
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    References listed on IDEAS

    as
    1. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    2. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    3. Irene Gijbels & Peter Hall & Aloïs Kneip, 1999. "On the Estimation of Jump Points in Smooth Curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 231-251, June.
    4. Astrid Dempfle & Winfried Stute, 2002. "Nonparametric estimation of a discontinuity in regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 233-242, May.
    5. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 1999. "Testing for Changes in Multivariate Dependent Observations with an Application to Temperature Changes," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 96-119, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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