Another Look At Ridge Calibration

摘要

When using calibration estimators, it may be desirable to meet not only benchmark constraints but also range restrictions on the weight adjustments. This can be achieved by a suitable choice of the distance function underlying calibration. However, iterative algorithms are usually needed to solve this calibration problem and convergence within a reasonable number of iterations is not necessarily guaranteed. Ridge calibration can offer an alternative solution to this problem as well as the method of Chen, Sitter and Wu (2002). In both cases, benchmark constraints are relaxed so as to satisfy range restrictions. First, we establish the connection between both methods when the usual chi-square distance function is used. We also propose an alternative method and show its equivalence to ridge calibration. This equivalence can be employed to justify the use of ridge calibration over the Chen, Sitter and Wu method if staying close to the known benchmark totals is a desirable goal. A numerical illustration is given using data from the Canadian Survey of Labour and Income Dynamics. Finally, we consider more general distance functions, which we propose to minimise using a simple iteratively reweighted chi-square algorithm in the same spirit as the iteratively reweighted least-squares algorithm is used to solve nonlinear estimating equations.