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Minimum Risk Point Estimation of Gini Index


This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost at the same time. In this article, a purely sequential procedure is proposed which provides an estimate of the sample size required to achieve a sufficiently smaller estimation error and lower sampling cost. Characteristics of the purely sequential procedure are examined and asymptotic optimality properties are proved without assuming any specific distribution of the data. Performance of our method is examined through extensive simulation study.

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We are grateful to the associate editor and the two anonymous referees for their valuable feedback that helped us improve this manuscript. We also thank Prof. Amarendra Das for providing the income data, which helped us show an application of the proposed method of this article.

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Correspondence to Shyamal K. De.

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De, S.K., Chattopadhyay, B. Minimum Risk Point Estimation of Gini Index. Sankhya B 79, 247–277 (2017).

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Keywords and phrases.

  • Asymptotic efficiency
  • Ratio regret
  • Reverse submartingale
  • Sequential point estimation
  • Simple random sampling
  • U-statistics

AMS (2000) subject classification.

  • Primary: 62L12
  • 62G05
  • Secondary: 60G46
  • 60G40
  • 91B82