Modeling Concentration and Dispersion in Multiple Regression
We consider concepts and models that are useful for measuring how strongly the distribution of a positive response Y is concentrated near a value with a focus on how concentration varies as a function of covariates. We combine ideas from statistics, economics and reliability theory. Lorenz introduced a device for measuring inequality in the distribution of incomes that indicate how much the incomes below the uth quantile fall short of the egalitarian situation where everyone has the same income. Gini introduced an index that is the average over u of the difference between the Lorenz curve and its values in the egalitarian case. More generally, we can think of the Lorenz and Gini concepts as measures of concentration that applies to other response variables in addition to incomes, e.g. wealth, sales, dividends, taxes, test scores, precipitation, and crop yield. In this paper we propose modified versions of the Lorenz and Gini measures of concentration that we relate to statistical concepts of dispersion. Moreover, we consider the situation where the measures of concentration/dispersion are functions of covariates. We consider the estimation of these functions for parametric models and a semiparametric model involving regression coefficients and an unknown baseline distribution. In this semiparametric model, which combines ideas from Pareto, Lehmann and Cox, we find partial likelihood estimates of the regression coefficients and the baseline distribution that can be used to construct estimates of the various measures of concentration/dispersion.
|Date of creation:||Mar 2005|
|Contact details of provider:|| Postal: P.O.Box 8131 Dep, N-0033 Oslo, Norway|
Phone: (+47) 21 09 00 00
Fax: +47 - 62 88 55 95
Web page: http://www.ssb.no/en/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Giovanni Maria Giorgi & Riccardo Mondani, 2005. "Sampling distribution of the Bonferroni inequality index from exponential population," Econometrics 0507008, EconWPA.
- Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
- Michael Sattinger (ed.), 2001. "Income Distribution," Books, Edward Elgar Publishing, volume 0, number 2018.
- Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
- Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
When requesting a correction, please mention this item's handle: RePEc:ssb:dispap:412. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (L MaasÃ¸)
If references are entirely missing, you can add them using this form.