The optimization problem of quantile and poverty measures estimation based on calibration

New calibrated estimators of quantiles and poverty measures are proposed. These estimators combine the incorporation of auxiliary information provided by auxiliary variables related to the variable of interest by calibration techniques with the selection of optimal calibration points under simple random sampling without replacement. The problem of selecting calibration points that minimize the asymptotic variance of the quantile estimator is addressed. Once the problem is solved, the definition of the new quantile estimator requires that the optimal estimator of the distribution function on which it is based verifies the properties of the distribution function. Through a theorem, the nondecreasing monotony property for the optimal estimator of the distribution function is established and the corresponding optimal estimator can be defined. This optimal quantile estimator is also used to define new estimators for poverty measures. Simulation studies with real data from the Spanish living conditions survey compares the performance of the new estimators against various methods proposed previously, where some resampling techniques are used for the variance estimation. Based on the results of the simulation study, the proposed estimators show a good performance and are a reasonable alternative to other estimators.Ministerio de Educacion y Cienci

An Analysis of the Impact of Various Sampling Designs on the Headcount Index: A Simulation Study Based on the EU-SILC

The analysis and the comparison of poverty between regions and countries are important topics in social sciences, which have relevant demands of many national (Cáritas, Intermón Oxfam, Cruz Roja, etc) and international (UN, World Bank, OECD, Eurostat, IMF, etc) agencies and organizations. One of the most common poverty indicators in practice is the headcount index, which analyzes the proportion of individuals considered as poor in a population. In this paper, we first analyze the impact on the headcount index when different sampling designs are considered. Note that this study is based on real data sets taken from different countries of the European Union, and the empirical measures for comparisons are based on different Monte Carlo simulation studies. For instance, we observe that stratified sampling has the best performance in comparison to alternative sampling designs. Post-stratification performs similar to simple random sampling without replacement, and the use of auxiliary information provides similar results to ones derived from stratified sampling. Second, we also analyze the empirical performance of different variance estimators under the commented sampling designs. We conclude that they have a similar empirical performance, and they provide, in general, confidence intervals with desirable coverage rates