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.

提出了新的标定的分位数和贫困衡量指标。这些估算器结合了通过校准技术将与感兴趣变量有关的辅助变量提供的辅助信息与通过简单随机采样而不选择的最佳校准点的选择相结合。解决了选择校准点以最小化分位数估计器的渐近方差的问题。解决问题后，新分位数估计器的定义要求它所基于的分布函数的最佳估计器验证分布函数的属性。通过一个定理，建立了分布函数最优估计量的单调性质，并且可以定义相应的最优估计量。该最佳分位数估算器还用于定义贫困度量的新估算器。使用来自西班牙生活状况调查的真实数据进行的仿真研究将新估算器的性能与之前提出的各种方法进行了比较，在此之前，一些重新采样技术用于方差估算。根据仿真研究的结果，提出的估计器显示出良好的性能，并且是其他估计器的合理替代方案。