Stratification: Measuring and inference

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Abstract

Stratification of distribution functions is an important issue in the area of income distributions. Two distribution functions form a perfect stratification if they occupy disjoint ranges on the horizontal axis. Otherwise, there is overlapping. A measure which quantifies the amount of stratification is introduced by Yitzhaki (1994), but no procedure for drawing inference is suggested. We develop a consistent estimator of the degree of overlapping and offer a nonparametric procedure for inference. Its limiting distribution, properly standardized, is normal. The asymptotic variance can be estimated using the jackknife method, and simulations show that the suggested procedure works well for sample sizes of 50 (100 for some cases).

Original languageEnglish
Pages (from-to)2133-2145
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Volume34
Issue number11
DOIs
StatePublished - 21 Nov 2005

Keywords

  • Decomposition of Gini
  • Gini coefficient
  • Jackknife
  • Overlapping index
  • U-statistic

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