Survey Methodology
Linearization versus bootstrap for variance estimation of the change between Gini indexes

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by Guillaume Chauvet and Camelia GogaNote 1

  • Release date: June 21, 2018
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Abstract

This paper investigates the linearization and bootstrap variance estimation for the Gini coefficient and the change between Gini indexes at two periods of time. For the one-sample case, we use the influence function linearization approach suggested by Deville (1999), the without-replacement bootstrap suggested by Gross (1980) for simple random sampling without replacement and the with-replacement of primary sampling units described in Rao and Wu (1988) for multistage sampling. To obtain a two-sample variance estimator, we use the linearization technique by means of partial influence functions (Goga, Deville and Ruiz-Gazen, 2009). We also develop an extension of the studied bootstrap procedures for two-dimensional sampling. The two approaches are compared on simulated data.

Key Words:     Composite estimator; Horvitz-Thompson estimator; Influence function; Intersection estimator; Replication weights; Two-sample survey; Two-dimensional sampling design; Union estimator; Variance estimation.

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How to cite

Chauvet, G., and Goga, C. (2018). Linearization versus bootstrap for variance estimation of the change between Gini indexes. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 44, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2018001/article/54926-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2018

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. One sample case
Section 3. Two-sample case
Section 4. Simulation study
Section 5. Conclusion
Acknowledgements
Appendix
References

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