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
Section 1. Introduction

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The 2015 Mexican Intercensal survey (MIC2015) conducted by the National Institute of Statistics and Geography (INEGI, 2015) collected information nationwide, using a probability sampling design in 1,643 municipalities and through a census in 814 municipalities. In this study we use the census data corresponding to 441 municipalities from the state of Oaxaca.

We focus on income as the variable of interest which exhibits a nonresponse rate of about 22.5%. Considering the respondents, the distribution of income has a high skewness mainly due to the presence of extreme values, and shows some values with high frequency.

The objective of this study is to assess the empirical coverage rate of confidence intervals (CI) computed by three methods for the population mean and population quantiles, 0.1, 0.5 and 0.9, in survey data with nonresponse. Two-phase sampling is used with a random sample selected in the first phase, while in the second the sample is split into respondents and nonrespondents considering the nonresponse pattern of income in the census data. A response propensity model is used to adjust the weights for nonresponse.

For the population mean, we consider the Hájek estimator and two methods for computing CIs: empirical likelihood (Berger, 2020) and linearization (Särndal, Swenson and Wretman, 1992, Sections 5.2 and 5.7). Concerning the population quantiles, we consider the point estimator obtained by interpolation of the distribution function as in Woodruff (1952) and Graf and Tillé (2014), and three methods for computing CIs: empirical likelihood (Berger, 2020), Woodruff (Woodruff, 1952) and linearization (Deville, 1999). These methods are described in Section 2, the numerical results are presented in Section 3 for the MIC2015 data and in Section 4 for some simulated populations. Some final comments are given in Section 5.

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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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