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When large n is not enough – Distribution-free interval estimators for ratios of quantiles

Author

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  • Luke A. Prendergast

    (La Trobe University)

  • Robert G. Staudte

    (La Trobe University)

Abstract

Ratios of sample percentiles or of quantiles based on a single sample are often published for skewed income data to illustrate aspects of income inequality, but distribution-free confidence intervals for such ratios are not available in the literature. Here we derive and compare two large-sample methods for obtaining such intervals. They both require good distribution-free estimates of the quantile density at the quantiles of interest, and such estimates have recently become available. Simulation studies for various sample sizes are carried out for Pareto, lognormal and exponential distributions, as well as fitted generalized lambda distributions, to determine the coverage probabilities and widths of the intervals. Robustness of the estimators to contamination or a positive proportion of zero incomes is examined via influence functions and simulations. The motivating example is Australian household income data where ratios of quantiles measure inequality, but of course these results apply equally to data from other countries.

Suggested Citation

  • Luke A. Prendergast & Robert G. Staudte, 2017. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 277-293, September.
    • Handle: RePEc:kap:jecinq:v:15:y:2017:i:3:d:10.1007_s10888-017-9347-9
    DOI: 10.1007/s10888-017-9347-9
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    References listed on IDEAS

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    1. Robert Staudte, 2014. "Inference for quantile measures of skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 751-768, December.
    2. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    3. Kulinskaya, Elena & Morgenthaler, Stephan & Staudte, Robert G., 2010. "Variance Stabilizing the Difference of Two Binomial Proportions," The American Statistician, American Statistical Association, vol. 64(4), pages 350-356.
    4. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
    5. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
    6. Stephan Morgenthaler & Robert G. Staudte, 2012. "Advantages of Variance Stabilization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 714-728, December.
    7. Su, Steve, 2007. "Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i09).
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