Determining PP optimum calibration points to construct calibration estimators of the distribution function

Survey statisticians make use of auxiliary information to improve estimates, for example in calibration estimation, introduced in Deville and Särndal (1992), which is used to obtain new weights that are close to the basic design weights and that, at the same time, comply with benchmark constraints on the auxiliary information available. Rueda et al. (2007) applied this calibration technique to estimate the distribution function. This estimator of the distribution function is built by means of constraints that require the use of a set of fixed values t1,t2,…,tPt1,t2,…,tP. The precision of the resulting calibration estimator varies according to the selection of titi. In the present work, we study the problem of determining the optimal values titi that give the best possible estimation under simple random sampling without replacement.