IASS - Webinar 54: Debiased Calibration Estimation Using Generalised Entropy in Survey Sampling

Incorporating the auxiliary information into the survey estimation is a fundamental problem in survey sampling. Calibration weighting is a popular tool for incorporating the auxiliary information. The calibration weighting method of Deville and Sarndal (1992) uses a distance measure between the design weights and the final weights to solve the optimisation problem with calibration constraints. In this talk, we first present the calibration weighting problem as a projection onto a subspace of calibration weights. After that, we propose a new framework using generalised entropy as the objective function for optimisation. Design weights are used in the constraints, rather than in the objective function, to achieve design consistency. The new calibration framework is attractive as it is general and can produce more efficient calibration weights than the classical calibration weights. Furthermore, we identify the optimal choice of the generalised entropy function that achieves the minimum variance among the different choices of the generalised entropy function under the same constraints. Asymptotic properties, such as design consistency and asymptotic normality, are presented rigorously. The results from a limited simulation study are also presented.