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Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

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  • Vijay Verma
  • Gianni Betti

Abstract

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.

Suggested Citation

  • Vijay Verma & Gianni Betti, 2011. "Taylor linearization sampling errors and design effects for poverty measures and other complex statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1549-1576, August.
  • Handle: RePEc:taf:japsta:v:38:y:2011:i:8:p:1549-1576
    DOI: 10.1080/02664763.2010.515674
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    Citations

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    Cited by:

    1. Gianni Betti, 2017. "What impact has the economic crisis had on quality of life in Europe? A multidimensional and fuzzy approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 351-364, January.
    2. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    3. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    4. Gianni Betti & Rossella Soldi & Ilija Talev, 2016. "Fuzzy Multidimensional Indicators of Quality of Life: The Empirical Case of Macedonia," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 127(1), pages 39-53, May.
    5. Asma Zedini & Besma Belhadj, 2015. "A New Approach to Unidimensional Poverty Analysis: Application to the Tunisian Case," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 465-476, September.
    6. Gianni Betti & Francesca Gagliardi & Achille Lemmi & Vijay Verma, 2015. "Comparative measures of multidimensional deprivation in the European Union," Empirical Economics, Springer, vol. 49(3), pages 1071-1100, November.
    7. repec:eee:regeco:v:66:y:2017:i:c:p:175-184 is not listed on IDEAS
    8. Berger Yves G. & Munoz Juan F., 2015. "On Estimating Quantiles Using Auxiliary Information," Journal of Official Statistics, De Gruyter Open, vol. 31(1), pages 101-119, March.
    9. Brzezinski, Michal, 2013. "Asymptotic and bootstrap inference for top income shares," Economics Letters, Elsevier, vol. 120(1), pages 10-13.
    10. Oguz Alper Melike & Berger Yves G., 2015. "Variance Estimation of Change in Poverty Rates: an Application to the Turkish EU-SILC Survey," Journal of Official Statistics, De Gruyter Open, vol. 31(2), pages 155-175, June.
    11. Betti Gianni, 2014. "The effect of equivalence scales on poverty at Oblast level in Ukraine," Экономика региона, CyberLeninka;Федеральное государственное бюджетное учреждение науки «Институт экономики Уральского отделения Российской академии наук», issue 2, pages 78-88.
    12. Crescenzi Federico & Betti Gianni & Gagliardi Francesca, 2016. "Comparing small area techniques for estimating poverty measures: the case study of Austria and Spain," Экономика региона, CyberLeninka;Федеральное государственное бюджетное учреждение науки «Институт экономики Уральского отделения Российской академии наук», vol. 12(2), pages 396-404.
    13. Federico Crescenzi & Gianni Betti & Francesca Gagliardi, 2015. "Comparing small area techniques for estimating poverty measures," Department of Economics University of Siena 721, Department of Economics, University of Siena.
    14. Vincenzo Salvucci & Gianni Betti & Francesca Gagliardi, 2012. "Multidimensional and Fuzzy Measures of Poverty and Inequality at National and Regional Level in Mozambique," Department of Economics University of Siena 649, Department of Economics, University of Siena.

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