Use of auxiliary information by calibration on distribution function.

Summary This research concerns the use of auxiliary information in survey theory. The fact that there is no UMVUE (unbiased estimator with uniformly minimum variance) for the total and the lack of information about the likelihood function force survey statisticians to use specific techniques to construct more efficient estimators, among which are the ratio estimator, the regression estimator and the margin calibration estimator. Sometimes, we have complete auxiliary information, in the form of distribution functions of real variables. This information is much more detailed than the knowledge of the totals alone. The margin calibration method therefore requires an adaptation to use the knowledge of distribution functions, which is equivalent to a much larger, possibly infinite, number of totals. The main objective of this research is to generalize the margin calibration technique by developing methods for using this information, called distribution function calibration methods. Three approaches have been proposed: parametric, semi-parametric and non-parametric calibration. Generalizations to rank calibration and moment calibration are also proposed. An in-depth study on two-stage, two-phase and two-dimensional systematic sampling is also provided as systematic sampling is a special case. A study on the estimation of the distribution function and the fractiles of a finite population is presented in the last chapter because the estimation of the distribution function is a component of some methods developed for the calibration on the distribution function. On the other hand, the estimation of the distribution function and fractiles of a finite population is in itself an interesting topic in survey theory, to which survey statisticians have recently given much attention. Numerical examples on simulated and real data are presented to test the different methods developed in this research. The simulations show that the distribution function estimators are in general more accurate than the marginally calibrated estimator.