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Simultaneous Density Estimation of Several Income Distributions

Author

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  • Marron, J.S.
  • Schmitz, H.-P.

Abstract

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(4), pages 476-488, December.
    • Handle: RePEc:cup:etheor:v:8:y:1992:i:04:p:476-488_01
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. C�line Bonnefond & Matthieu Cl�ment, 2012. "An analysis of income polarisation in rural and urban China," Post-Communist Economies, Taylor & Francis Journals, vol. 24(1), pages 15-37, June.
    7. 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.
    8. Roberto Zelli & Maria Grazia Pittau, 2006. "Empirical evidence of income dynamics across EU regions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 605-628.
    9. 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.
    10. 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.
    11. Leone Leonida, 2024. "Visualizing Convergence Dynamics across Regions and States: h -Convergence," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    12. Leone Leonida & Antonio Giangreco & Sergio Scicchitano & Marco Biagetti, 2023. "Britain and BrExit: Is the UK more attractive to supervisors? An analysis of the wage premium to supervision across the EU," British Journal of Industrial Relations, London School of Economics, vol. 61(2), pages 291-312, June.
    13. 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).
    14. 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.
    15. Zhengwu Zhang & Eric Klassen & Anuj Srivastava, 2019. "Robust Comparison of Kernel Densities on Spherical Domains," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 144-171, February.
    16. Jose Ameijeiras-Alonso & Rosa M. Crujeiras & Alberto Rodríguez-Casal, 2019. "Mode testing, critical bandwidth and excess mass," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 900-919, September.
    17. Mills, Bradford F. & Alwang, Jeffrey Roger & Hazarika, Gautam, 2000. "The Impact Of Welfare Reform Across Metropolitan And Non-Metropolitan Areas: A Non-Parametric Analysis," 2000 Annual meeting, July 30-August 2, Tampa, FL 21760, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    18. Biagetti, Marco & Giangreco, Antonio & Leonida, Leone & Scicchitano, Sergio, 2020. "BrExit or BritaIn: Is the UK more Attractive to Supervisors? An Analysis of Wage Premium to Supervision across the EU," GLO Discussion Paper Series 510, Global Labor Organization (GLO).
    19. 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.
    20. J. S. Marron & Frederic Udina, 1995. "Interactive local bandwidth choice," Economics Working Papers 109, Department of Economics and Business, Universitat Pompeu Fabra.
    21. 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.
    22. 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.
    23. 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).
    24. 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.
    25. 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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