Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-12T04:28:54.723Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous Density Estimation of Several Income Distributions

Published online by Cambridge University Press:  18 October 2010

J.S. Marron  and
H.-P. Schmitz
J.S. Marron
Affiliation:
University of Bonn
H.-P. Schmitz
Affiliation:
University of Bonn
Get access Rights & Permissions [Opens in a new window]

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.

Type
Articles
Information
Econometric Theory , Volume 8 , Issue 4 , December 1992 , pp. 476 - 488
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Blinder, A.S. The level and distribution of income well-being. In Feldstein, M. (ed.), The American Economy in Transition. Chicago: University of Chicago Press, 1980.Google Scholar
2.Bowman, A.An alternative method of cross-validation for the smoothing of density estimates. Biometrika 17 (1984): 353–360.CrossRefGoogle Scholar
3.Göseke, G. & Bedau, K.D.. Verteilung und Schichtung der Einkommen der privaten Haushalte in der BRD von 1950–1975. Duetsches Institut für Wirtschaftsforschung, Heft 31. Duncker and Humblot, Berlin, 1974.Google Scholar
4.Hall, P. & Marron, J.S.. Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation. Probability Theory and Related Fields 74 (1987): 567–581.CrossRefGoogle Scholar
5.Hartog, J. & Venbergen, J.G.. Dutch treat, long-run changes in personal income distribution. De Economist 126, No. 4 (1978): 521–549.CrossRefGoogle Scholar
6.Henninger, C. & Schmitz, H.P.. Size distributions of incomes and expenditures: Testing the parametric approach; Discussion paper A-219 SFB 303, Universität Bonn, 1989.Google Scholar
7.Hirschberg, J.G., Molina, D.J. & Slottje, D.J.. A selection criterion for choosing between functional forms of income distributions. Econometric Reviews 1 (1989): 183–197.Google Scholar
8.Hirschberg, J.G., Scully, G.W. & Slottje, D.J.. Efficiency aspects of the major league baseball players market. To appear in Economics of Sports, Rottenberg, C. (ed.). Chicago: Chicago Press, 1991.Google Scholar
9.Hirschberg, J.G., Scully, G.W. & Slottje, D.J.. A test of the efficient labor market hypothesis: The case of major league baseball; unpublished manuscript, 1991.Google Scholar
10.Hoel, P.G.Introduction to Mathematical Statistics. New York: Wiley, 1971.Google Scholar
11.McDonald, J.B.Some generalized functions for the size distribution of income. Econometrica 52, No. 3 (1984): 647–663.CrossRefGoogle Scholar
12.Marron, J.S.Automatic smoothing parameter selection: A survey. Empirical Economics 13 (1988): 187–208.CrossRefGoogle Scholar
13.Marron, J.S.Partitioned cross-validation. Economic Reviews 6 (1988): 271–283.CrossRefGoogle Scholar
14.Nygard, F. & Sandstrom, A.. Income inequality measures based on sample surveys. Journal of Econometrics 42 (1989): 81–95.CrossRefGoogle Scholar
15.Park, B.U. & Marron, J.S.. Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association 85 (1990): 66–72.CrossRefGoogle Scholar
16.Rudemo, M.Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics 9 (1982): 65–78.Google Scholar
17.Scott, D.W. & Terrell, G.R.. Biased and unbiased cross-validation in density estimation. Journal of the American Statistical Association 82 (1987): 1131–1146.CrossRefGoogle Scholar
18.Silverman, B.W.Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall, 1986.Google Scholar
19.Singh, S.K. & Maddala, G.S.. A function for size distributions of incomes. Econometrica 44 (1976): 963–970.CrossRefGoogle Scholar
20.Terrell, G.R.The maximal smoothing principle in density estimation. Journal of the American Statistical Association 85 (1990): 470–477.CrossRefGoogle Scholar