| Summary: | The analysis of sample surveys is one of the key areas in official statistics. An integral part of analysing sample data is choosing appropriate weights for each sample member. These weights can informally be thought of as the number of population members each person in the sample represents. Calibration is a method that adjusts the weights assigned to sample members in order to satisfy (or approximately satisfy) some pre-determined constraints. These are typically based on Census data or other large surveys. The key idea is that estimates formed from the weighted sample should replicate the known values from other sources. This thesis begins with the mathematical formulation of the calibration problem as an optimization problem. Whilst the calibration problem has been defined in existing calibration literature, it has not been clearly formulated as a problem in optimization. New calibration functions are also presented, and an outline of their benefits compared to existing calibration functions given. Much of the calibration literature focuses on so-called hard calibration. This requires an exact matching between the weighted sample data and the pre-determined constraints. However, relaxing this condition can often lead to more “well-behaved” solutions. This is the idea behind soft calibration, which has received less attention in existing literature. In this thesis, soft calibration is formulated using an optimization framework, and also presented as a diagnostic tool for identifying problematic constraints. For many practitioners, the variance (and mean square error) of the estimates obtained is of particular interest. This is the motivation for a new approach to calibration that seeks to directly minimize the mean square error of the calibration estimator. This method is compared with existing calibration techniques, and future research directions for this approach are considered.
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