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Kernel density estimation for heaped data

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  • Groß, Marcus
  • Rendtel, Ulrich

Abstract

In self-reported data usually a phenomenon called 'heaping' occurs, i.e. survey participants round the values of their income, weight or height to some degree. Additionally, respondents may be more prone to round off or up due to social desirability. By ignoring the heaping process a severe bias in terms of spikes and bumps is introduced when applying kernel density methods naively to the rounded data. A generalized Stochastic Expectation Maximization (SEM) approach accounting for heaping with potentially asymmetric rounding behaviour in univariate kernel density estimation is presented in this work. The introduced methods are applied to survey data of the German Socio-Economic Panel and exhibit very good performance simulations.

Suggested Citation

  • Groß, Marcus & Rendtel, Ulrich, 2015. "Kernel density estimation for heaped data," Discussion Papers 2015/27, Free University Berlin, School of Business & Economics.
    • Handle: RePEc:zbw:fubsbe:201527
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    References listed on IDEAS

    as
    1. Pudney, Stephen, 2008. "Heaping and leaping: survey response behaviour and the dynamics of self-reported consumption expenditure," ISER Working Paper Series 2008-09, Institute for Social and Economic Research.
    2. Erich Battistin & Raffaele Miniaci & Guglielmo Weber, 2003. "What Do We Learn from Recall Consumption Data?," Journal of Human Resources, University of Wisconsin Press, vol. 38(2).
    3. Groß, Marcus & Rendtel, Ulrich & Schmid, Timo & Schmon, Sebastian & Tzavidis, Nikos, 2015. "Estimating the density of ethnic minorities and aged people in Berlin: Multivariate kernel density estimation applied to sensitive geo-referenced administrative data protected via measurement error," Discussion Papers 2015/7, Free University Berlin, School of Business & Economics.
    4. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    5. Steffen Otterbach & Alfonso Sousa-Poza, 2010. "How Accurate are German Work-time Data? A Comparison of Time-diary Reports and Stylized Estimates," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 97(3), pages 325-339, July.
    6. repec:mpr:mprres:6195 is not listed on IDEAS
    7. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    8. Jan Marcus & Rainer Siegers & Markus M. Grabka, 2013. "Preparation of Data from the New SOEP Consumption Module: Editing, Imputation, and Smoothing," Data Documentation 70, DIW Berlin, German Institute for Economic Research.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Heaping; Survey Data; Measurement error; Self-reported data; Kernel density estimation; Rounded data;
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