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Simultaneous Density Estimation of Several Income Distributions


  • Marron, J.S.
  • Schmitz, H.-P.


The size distributions of net income in Great Britain changed systematically in the 1970s. This can be shown by visual comparison of nonparametric density estimates. Typical bandwidth selection methods, such as least squares and biased cross-validation, tend to hinder comparison, because of too much variability across curves. Hence, a method for finding an appropriate pooled bandwidth is developed. It is seen that this method is much more reliable than single curve cross-validation.

Suggested Citation

  • Marron, J.S. & Schmitz, H.-P., 1992. "Simultaneous Density Estimation of Several Income Distributions," Econometric Theory, Cambridge University Press, vol. 8(04), pages 476-488, December.
  • Handle: RePEc:cup:etheor:v:8:y:1992:i:04:p:476-488_01

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    Cited by:

    1. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    2. David Neumark & Mark Schweitzer & William Wascher, 2005. "The Effects of Minimum Wages on the Distribution of Family Incomes: A Nonparametric Analysis," Journal of Human Resources, University of Wisconsin Press, vol. 40(4), pages 867-894.
    3. Balaguer-Coll, Maria Teresa & Prior, Diego & Tortosa-Ausina, Emili, 2007. "On the determinants of local government performance: A two-stage nonparametric approach," European Economic Review, Elsevier, vol. 51(2), pages 425-451, February.
    4. Leone Leonida & Leone Leonida & Daniel Montolio, 2003. "Public Capital, Growth and Convergence in Spain. A Counterfactual Density Estimation Approach," Working Papers 2003/3, Institut d'Economia de Barcelona (IEB).
    5. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2008. "Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 149-184, June.
    6. Flachaire, Emmanuel & Núñez, Olivier, 2003. "Estimation of income distribution and detection of subpopulations: an explanatory model," DES - Working Papers. Statistics and Econometrics. WS ws030201, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Duc Devroye & J. Beirlant & R. Cao & R. Fraiman & P. Hall & M. Jones & Gábor Lugosi & E. Mammen & J. Marron & C. Sánchez-Sellero & J. Uña & F. Udina & L. Devroye, 1997. "Universal smoothing factor selection in density estimation: theory and practice," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-320, December.
    8. Bradford Mills & Jeffrey R. Alwang & Gautam Hazarika, 2000. "The Impact of Welfare Reform Across Metropolitan and Nonmetropolitan Areas: A Nonparametric Analysis," JCPR Working Papers 183, Northwestern University/University of Chicago Joint Center for Poverty Research.
    9. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    10. Charpentier, Arthur & Flachaire, Emmanuel, 2015. "Log-Transform Kernel Density Estimation Of Income Distribution," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 141-159, Mars-Juin.
    11. Jenkins, Stephen P., 1995. "Did the middle class shrink during the 1980s? UK evidence from kernel density estimates," Economics Letters, Elsevier, vol. 49(4), pages 407-413, October.
    12. Céline Bonnefond & Matthieu Clément, 2012. "An analysis of income polarisation in rural and urban China," Post-Communist Economies, Taylor & Francis Journals, vol. 24(1), pages 15-37, June.
    13. Priebe, Carey E. & Marchette, David J., 2000. "Alternating kernel and mixture density estimates," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 43-65, November.
    14. Riccardo Massari, 2009. "Is income becoming more polarized Italy? A closer look with a distributional approach," Working Papers 1, Doctoral School of Economics, Sapienza University of Rome.
    15. Leonede Leonida & Daniel Montolio, "undated". "Inter-Distributional and Intra-Clusters Dynamics, and Territorial Distribution of Growth among Spanish Provinces," Studies on the Spanish Economy 109, FEDEA.
    16. J. S. Marron & Frederic Udina, 1995. "Interactive local bandwidth choice," Economics Working Papers 109, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Leone Leonida & Daniel Montolio, 2001. "Convergence and Inter-Distributional Dynamics among the Spanish Provinces. A Non-parametric Density Estimation Approach," Working Papers 2001/7, Institut d'Economia de Barcelona (IEB).
    18. Giovanni Caggiano & Leone Leonida, 2013. "Multimodality in the distribution of GDP and the absolute convergence hypothesis," Empirical Economics, Springer, vol. 44(3), pages 1203-1215, June.
    19. Leone Leonida & Daniel Montolio, 2004. "On the determinants of convergence and divergence processes in Spain," Investigaciones Economicas, Fundación SEPI, vol. 28(1), pages 89-121, January.

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