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Density Estimation For Clustered Data

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  • Robert Breunig

Abstract

The commonly used survey technique of clustering introduces dependence into sample data. Such data is frequently used in economic analysis, though the dependence induced by the sample structure of the data is often ignored. In this paper, the effect of clustering on the non-parametric, kernel estimate of the density, f(x), is examined. The window width commonly used for density estimation for the case of i.i.d. data is shown to no longer be optimal. A new optimal bandwidth using a higher-order kernel is proposed and is shown to give a smaller integrated mean squared error than two window widths which are widely used for the case of i.i.d. data. Several illustrations from simulation are provided.

Suggested Citation

  • Robert Breunig, 2001. "Density Estimation For Clustered Data," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 353-367.
    • Handle: RePEc:taf:emetrv:v:20:y:2001:i:3:p:353-367
    DOI: 10.1081/ETC-100104939
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    References listed on IDEAS

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    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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    2. David Gunawan & William Griffths & Anatasios Panagiotelis and Duangkamon Chotikapanich, 2017. "Bayesian Weighted Inference from Surveys "Abstract: Data from large surveys are often supplemented with sampling weights that are designed to reflect unequal probabilities of response and selecti," Department of Economics - Working Papers Series 2030, The University of Melbourne.
    3. Sayed A. Mostafa & Ibrahim A. Ahmad, 2019. "Kernel density estimation from complex surveys in the presence of complete auxiliary information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 295-338, April.
    4. Breunig, Robert, 2008. "Nonparametric density estimation for stratified samples," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2194-2200, October.
    5. Daniel J. Henderson & Christopher F. Parmeter & R. Robert Russell, 2008. "Modes, weighted modes, and calibrated modes: evidence of clustering using modality tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 607-638.

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