Fall Seminar Series - October 16, 2003
University
of Minnesota
School
of Statistics
College
of Liberal Arts
Lorenz, Gini, Bonferroni and Quantile
Regression
Kjell Doksum
Department of Statistics
University of California, Berkeley
Thursday, October 16, 2003
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
Lorenz and Bonferroni introduced measures of the concentration of
income that indicate how much the incomes below the uth quantile fall short
of the egalitarian situation where everyone has the same income.As u changes,these
measures become curves on [0,1].Gini introduced an index that is the average
over u of the difference between the Lorenz curve and its egalitarian version.Bonferroni
similarly introduced an index based on the Bonferroni curve.In this paper
we consider the situation where the income distribution depends on covariates.In
this case the Lorenz and Bonferroni curves as well as the Gini and Bonferroni
indices are functions of the covariates.We consider the estimation of these
functions for parametric,semiparametric and nonparametric models.In particular,we
consider a semiparametric model involving regression coefficients and
an unknown baseline income distribution.In this model we find partial likelihood
estimates of the regression coefficients and the baseline distribution
that can be used to construct estimates of the Gini and Bonferroni indices.
We also consider nonparametric models where nonparametric quantile regression
estimators can be used to estimate Lorenz,Gini,and Bonferroni regression.This
is joint work with Rolf Aaberge and Steinar Bjerve.