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Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation

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  • Dai, J.
  • Sperlich, S.

Abstract

In both nonparametric density estimation and regression, the so-called boundary effects, i.e. the bias and variance increase due to one sided data information, can be quite serious. For estimation performed on transformed variables this problem can easily get boosted and may distort substantially the final estimates, and consequently the conclusions. After a brief review of some existing methods a new, straightforward and very simple boundary correction is proposed, applying local bandwidth variation at the boundaries. The statistical behavior is discussed and the performance for density and regression estimation is studied for small and moderate sample sizes. In a simulation study this method is shown to perform very well. Furthermore, it appears to be excellent for estimating the world income distribution, and Engel curves in economics.

Suggested Citation

  • Dai, J. & Sperlich, S., 2010. "Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2487-2497, November.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2487-2497
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    References listed on IDEAS

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    1. Hajo Holzmann & Sebastian Vollmer & Julian Weisbrod, 2007. "Perspectives on the World Income Distribution - Beyond Twin Peaks Towards Welfare Conclusions," Ibero America Institute for Econ. Research (IAI) Discussion Papers 158, Ibero-America Institute for Economic Research.
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    4. Xavier Sala-i-Martin, 2006. "The World Distribution of Income: Falling Poverty and … Convergence, Period," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 351-397.
    5. Joachim Engel & Alois Kneip, 1996. "Recent approaches to estimating Engel curves," Journal of Economics, Springer, vol. 63(2), pages 187-212, June.
    6. Hall, Peter, 1983. "On near neighbour estimates of a multivariate density," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 24-39, March.
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    Cited by:

    1. Afonso, António & Arghyrou, Michael G. & Gadea, María Dolores & Kontonikas, Alexandros, 2018. "“Whatever it takes” to resolve the European sovereign debt crisis? Bond pricing regime switches and monetary policy effects," Journal of International Money and Finance, Elsevier, vol. 86(C), pages 1-30.
    2. Bernoth, Kerstin & Erdogan, Burcu, 2012. "Sovereign bond yield spreads: A time-varying coefficient approach," Journal of International Money and Finance, Elsevier, vol. 31(3), pages 639-656.
    3. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
    4. Michael G. Arghyrou & Maria Dolores Gadea, 2019. "Private bank deposits and macro/fiscal risk in the euro-area," CESifo Working Paper Series 7532, CESifo Group Munich.
    5. Arora, Siddharth & Taylor, James W., 2016. "Forecasting electricity smart meter data using conditional kernel density estimation," Omega, Elsevier, vol. 59(PA), pages 47-59.
    6. Charles Braymen & Eddery Lam, 2014. "Income Distribution and the Composition of Imports," The International Trade Journal, Taylor & Francis Journals, vol. 28(2), pages 121-139, June.
    7. Rodrigues, G.S. & Nott, David J. & Sisson, S.A., 2016. "Functional regression approximate Bayesian computation for Gaussian process density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 229-241.
    8. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    9. António Afonso & Michael G. Arghyrou & María Dolores Gadea & Alexandros Kontonikas, 2017. ""Whatever it takes" to Resolve the European Sovereign Debt Crisis? Bond Pricing Regime Switches and Monetary Policy Effects," CESifo Working Paper Series 6691, CESifo Group Munich.
    10. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    11. Gery Geenens, 2014. "Probit Transformation for Kernel Density Estimation on the Unit Interval," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 346-358, March.
    12. Machado, José A.F. & Santos Silva, J.M.C. & Wei, Kehai, 2016. "Quantiles, corners, and the extensive margin of trade," European Economic Review, Elsevier, vol. 89(C), pages 73-84.

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