Deville and Särndal's calibration: revisiting a 25 years old successful optimization problem

In 1992, in a famous paper, Deville and Särndal proposed the calibration method in order to adjust samples on known population totals. This paper had a very important impact in the theory and practise of survey statistics. In this paper, we propose a rigorous formalization of the calibration problem viewed as an optimization problem. We examine the main calibration functions and we discuss the question of the existence of solutions. We also propose an alternate way of solving the optimization problem given by the calibration principle. We finally present a set of simulations in order to compare the different methods.