Optimal dimension and optimal auxiliary vector to construct calibration estimators of the distribution function

The calibration technique (Deville and Särndal, 1992) to estimate the finite distribution function has been studied in several papers. Calibration seeks for new weights close enough to sampling weights according to some distance function and that, at the same time, match benchmark constraints on available auxiliary information. The non smooth character of the finite population distribution function causes certain complexities that are resolved by different authors in different ways. One of these is to have consistency at a number of arbitrarily chosen points. This paper deals with the problem of the optimal selection of the number of points and with the optimal selections of these points, when auxiliary information is used by means of calibration.