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

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.