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Journal of Global Optimization

, Volume 52, Issue 3, pp 471–485 | Cite as

Calibration of estimator-weights via semismooth Newton method

  • Ralf T. Münnich
  • Ekkehard W. Sachs
  • Matthias WagnerEmail author
Article

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.

Keywords

Semismooth Newton method Calibration Convex objective function General regression estimator Sample weights 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Ralf T. Münnich
    • 1
  • Ekkehard W. Sachs
    • 2
  • Matthias Wagner
    • 3
    Email author
  1. 1.Forumstat and Department of EconomicsUniversity of TrierTrierGermany
  2. 2.Forumstat and Department of MathematicsUniversity of TrierTrierGermany
  3. 3.Forumstat—Research Center for Regional and Environmental StatisticsUniversity of TrierTrierGermany

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