Calibration of estimator-weights via semismooth Newton method

Authors:
Ralf T. Münnich;Ekkehard W. Sachs;Matthias Wagner
Affiliations:
Forumstat and Department of Economics, University of Trier, Trier, Germany 54286;Forumstat and Department of Mathematics, University of Trier, Trier, Germany 54286;Forumstat--Research Center for Regional and Environmental Statistics, University of Trier, Trier, Germany 54286
Venue:
Journal of Global Optimization
Year:
2012

Citing 6
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Abstract

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.