Survey Methodology
Assessing the coverage of confidence intervals under nonresponse. A case study on income mean and quantiles in some municipalities from the 2015 Mexican Intercensal Survey

by Omar De La Riva Torres, Gonzalo Pérez-de-la-Cruz and Guillermina Eslava-GómezNote 1

  • Release date: January 6, 2022
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Abstract

This note presents a comparative study of three methods for constructing confidence intervals for the mean and quantiles based on survey data with nonresponse. These methods, empirical likelihood, linearization, and that of Woodruff’s (1952), were applied to data on income obtained from the 2015 Mexican Intercensal Survey, and to simulated data. A response propensity model was used for adjusting the sampling weights, and the empirical performance of the methods was assessed in terms of the coverage of the confidence intervals through simulation studies. The empirical likelihood and linearization methods had a good performance for the mean, except when the variable of interest had some extreme values. For quantiles, the linearization method had a poor performance, while the empirical likelihood and Woodruff methods had a better one, though without reaching the nominal coverage when the variable of interest had values with high frequency near the quantile of interest.

Key Words:   Confidence interval estimation; Empirical likelihood; Linearization; Missing at random; Nonresponse; Two-phase sampling.

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How to cite

De La Riva Torres, O., Pérez-de-la-Cruz, G. and Eslava-Gómez, G. (2021). Assessing the coverage of confidence intervals under nonresponse. A case study on income mean and quantiles in some municipalities from the 2015 Mexican Intercensal Survey. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 47, No. 2. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2021002/article/00004-eng.htm.

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ISSN : 1492-0921

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Published by authority of the Minister responsible for Statistics Canada.

© His Majesty the King in Right of Canada as represented by the Minister of Industry, 2022

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Catalogue No. 12-001-X

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Three methods for estimating confidence intervals
Section 3. Empirical study based on data from the populations MIC2015_Oax and MIC2015_Oaxtrunc
Section 4. Simulated populations
Section 5. Conclusions
Acknowledgements
References

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