Optimum calibration points estimating distribution functions

The calibration method has been widely discussed in the recent literature on survey sampling, and calibration estimators are routinely computed by many survey organizations. The calibration technique was introduced in [12] to estimate linear parameters as mean or total. Recently, some authors have applied the calibration technique to estimate the finite distribution function and the quantiles. The computationally simpler method in [14] is built by means of constraints that require the use of a fixed value t₀. The precision of the resulting calibration estimator changes with the selected point t₀. In the present paper, we study the problem of determining the optimal value t₀ that gives the best estimation under simple random sampling without replacement. A limited simulation study shows that the improvement of this optimal calibrated estimator over possible alternatives can be substantial.