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Gini’s mean difference and variance as measures of finite populations scales

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Abstract

We consider Gini’s mean difference statistic as an alternative to the empirical variance in the settings of finite populations, where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite-population context) estimation strategies for a scale of the population, related to the alternative statistic in a possible presence of outliers in the data.

The paper also presents a wide comparative survey of properties of Gini’s mean difference statistic and the empirical variance. It includes asymptotic properties of both statistics: the asymptotic normality, one-term Edgeworth expansions, and bootstrap approximations for Studentized versions of the statistics. Estimation of the variances and other parameters of the statistics is also studied, where we use auxiliary information available on the population elements. Theoretical results are illustrated by a simulation study.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos str. 4, LT-08663, Vilnius, Lithuania

    Andrius Čiginas

  2. Lithuanian University of Educational Sciences, Studentu˛ str. 39, LT-08106, Vilnius, Lithuania

    Dalius Pumputis

Authors
  1. Andrius Čiginas
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  2. Dalius Pumputis
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Correspondence to Andrius Čiginas.

Additional information

The research of A. Čiginas is supported by European Union Structural Funds project “Postdoctoral Fellowship Implementation in Lithuania.”

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Čiginas, A., Pumputis, D. Gini’s mean difference and variance as measures of finite populations scales. Lith Math J 55, 312–330 (2015). https://doi.org/10.1007/s10986-015-9283-y

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  • DOI: https://doi.org/10.1007/s10986-015-9283-y

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