Calibration of estimator‐weights via semismooth Newton method

Weighting is a common methodology in survey statistics to increase accuracy of estimates or to compensate for non‐response. One standard approach for weighting is calibration estimation which represents a common numerical problem. There are various approaches in the literature available, but quite a number of distance‐based approaches lack a mathematical justification or are numerically unstable. In this paper we reformulate the calibration problem as a system of nonlinear equations. Although the equations are lacking differentiability properties, one can show that they are semismooth and the corresponding extension of Newton’s method is applicable. This is a mathematically rigorous approach and the numerical results show the applicability of this method.