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dc.contributor.authorAaberge, Rolf
dc.contributor.authorBjerve, Steinar
dc.contributor.authorDoksum, Kjell
dc.date.accessioned2011-11-22T17:02:53Z
dc.date.available2011-11-22T17:02:53Z
dc.date.issued2005
dc.identifier.issn1892-753x
dc.identifier.urihttp://hdl.handle.net/11250/180275
dc.description.abstractWe consider concepts and models that are useful for measuring how strongly the distribution of a positive response Y is concentrated near a value y0 > 0 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. Keywords: Spread, concentration, Lorenz curve, Gini index, Lehmann model, Cox regression, Pareto model.no_NO
dc.language.isoengno_NO
dc.publisherStatistics Norway, Research Departmentno_NO
dc.relation.ispartofseriesDiscussion Papers;No. 412
dc.subjectGini indexno_NO
dc.subjectLehmann modelno_NO
dc.subjectLorenz curveno_NO
dc.subjectCox regressionno_NO
dc.subjectPareto modelno_NO
dc.subjectJEL classification: C14no_NO
dc.subjectJEL classification: D31no_NO
dc.subjectJEL classification: D63no_NO
dc.titleModeling concentration and dispersion in multiple regressionno_NO
dc.typeWorking paperno_NO
dc.subject.nsiVDP::Mathematics and natural science: 400::Mathematics: 410::Statistics: 412no_NO
dc.source.pagenumber19 s.no_NO


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