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Inference for Quantiles of a Finite Population: Asymptotic versus Resampling Results

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  • Pier Luigi Conti
  • Daniela Marella

Abstract

type="main" xml:id="sjos12122-abs-0001"> The aim of the paper is to study the problem of estimating the quantile function of a finite population. Attention is first focused on point estimation, and asymptotic results are obtained. Confidence intervals are then constructed, based on both the following: (i) asymptotic results and (ii) a resampling technique based on rescaling the ‘usual’ bootstrap. A simulation study to compare asymptotic and resampling-based results, as well as an application to a real population, is finally performed.

Suggested Citation

  • Pier Luigi Conti & Daniela Marella, 2015. "Inference for Quantiles of a Finite Population: Asymptotic versus Resampling Results," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 545-561, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:545-561
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    File URL: http://hdl.handle.net/10.1111/sjos.12122
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    References listed on IDEAS

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    1. Antal, Erika & Tillé, Yves, 2011. "A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 534-543.
    2. Jianqiang C. Wang & J. D. Opsomer, 2011. "On asymptotic normality and variance estimation for nondifferentiable survey estimators," Biometrika, Biometrika Trust, vol. 98(1), pages 91-106.
    3. Arindam Chatterjee, 2011. "Asymptotic properties of sample quantiles from a finite population," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 157-179, February.
    4. Sitter, Randy R. & Wu, Changbao, 2001. "A note on Woodruff confidence intervals for quantiles," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 353-358, May.
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    1. M. D. Jiménez-Gamero & J. L. Moreno-Rebollo & J. A. Mayor-Gallego, 2018. "On the estimation of the characteristic function in finite populations with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 95-121, March.
    2. Daniela Marella & Paola Vicard, 2022. "Bayesian network structural learning from complex survey data: a resampling based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 981-1013, October.
    3. Pier Luigi Conti & Alberto Iorio & Alessio Guandalini & Daniela Marella & Paola Vicard & Vincenzina Vitale, 2020. "On the estimation of the Lorenz curve under complex sampling designs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 1-24, March.
    4. Pier Luigi Conti & Fulvia Mecatti, 2022. "Resampling under Complex Sampling Designs: Roots, Development and the Way Forward," Stats, MDPI, vol. 5(1), pages 1-12, March.
    5. Omer Ozturk & Narayanaswamy Balakrishnan & Olena Kravchuk, 2023. "Order Statistics Based on a Combined Simple Random Sample from a Finite Population and Applications to Inference," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 77-101, February.
    6. Daniela Marella, 2018. "Pc Complex: Pc Algorithm For Complex Survey Data," Departmental Working Papers of Economics - University 'Roma Tre' 0240, Department of Economics - University Roma Tre.

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