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 5. Conclusions

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Considering the distribution of $y$ (income), it was observed that a poor performance of a method in the full response scenario generally corresponded to a poor one in the nonresponse scenario, although in several cases the coverage rate was larger in the latter. This suggests that having treated the ${\widehat{\varphi }}_k$ as fixed had little effect on the performance of the methods as compared to the impact of the characteristics of the distribution of $y.$ Extreme values were related to a low coverage of the CIs for the mean for both empirical likelihood and linearization methods. The presence of values with high frequency near a quantile of interest also had an impact on the coverage of its CIs; this might be related to the behavior of the step distribution function, where the jumps in $F\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>}$ and $\widehat{F}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>}$ are usually required to be small in order to obtain a good performance of the Woodruff method (Lohr, 2010, page 390). In general, the linearization method had a poor performance for quantiles, while the performance of empirical likelihood and of Woodruff were similar and better; this behavior has also been observed in Berger and De La Riva Torres (2016). While Woodruff method is simple and easy to implement, an advantage of the empirical likelihood method is that it can be used for parameters other than quantiles.

Acknowledgements

Omar De La Riva Torres was supported by the Post Doctoral Scholarship Program of the National Autonomous University of Mexico.

References

Berger, Y.G. (2020). An empirical likelihood approach under cluster sampling with missing observations. Annals of the Institute of Statistical Mathematics, 72, 91-121.

Berger, Y.G., and De La Riva Torres, O. (2016). Empirical likelihood confidence intervals for complex sampling designs. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78, 2, 319-341.

Deville, J.-C. (1999). Variance estimation for complex statistics and estimators: Linearization and residual techniques. Survey Methodology, 25, 2, 193-203. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/1999002/article/4882-eng.pdf.

Feller, W. (1968). An Introduction to Probability Theory and Its Applications: Volume I. New York: John Wiley & Sons, Inc.

Graf, E., and Tillé, Y. (2014). Variance estimation using linearization for poverty and social exclusion indicators. Survey Methodology, 40, 1, 61-79. Paper available at https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2014001/article/14000-eng.pdf.

Haziza, D., and Beaumont, J.-F. (2017). Construction of weights in surveys: A review. Statistical Science, 32, 2, 206-226.

INEGI (2015). Encuesta Intercensal 2015. Instituto Nacional de Estadística, Geografía e Informática. https://www.inegi.org.mx/programas/intercensal/2015/.

Kim, J.K., and Kim, J.J. (2007). Nonresponse weighting adjustment using estimated response probability. The Canadian Journal of Statistics, 35, 4, 501-514.

Lohr, S.L. (2010). Sampling: Design and Analysis. Brooks/Cole.

Osier, G. (2009). Variance estimation for complex indicators of poverty and inequality using linearization techniques. Survey Research Methods, 3, 3, 167-195.

Särndal, C.-E., Swenson, B. and Wretman, J.H. (1992). Model Assisted Survey Sampling. New York: Springer-Verlag.

Woodruff, R.S. (1952). Confidence intervals for medians and other position measures. Journal of the American Statistical Association, 47, 635-646.

Wu, C. (2004). Some algorithmic aspects of the empirical likelihood method in survey sampling. Statistica Sinica, 14, 1057-1067.

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