Reduction of optimal calibration dimension with a new optimal auxiliary vector for calibrated estimators of the distribution function

The calibration method has been widely used to incorporate auxiliary information in the estimation of various parameters. Specifically, some authors adapted this method to estimate the distribution function, although their proposal is computationally simple, its efficiency depends on the selection of an auxiliary vector of points. This work deals with the problem of selecting the calibration auxiliary vector that minimizes the asymptotic variance of the calibration estimator of distribution function. The optimal dimension of the optimal auxiliary vector is reduced considerably with respect to previous studies so that with a smaller set of points, the minimum of the asymptotic variance can be reached, which in turn allows to improve the efficiency of the estimates.