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The evaluation of variance component estimation software: generating benchmark problems by exact and approximate methods

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Abstract

The prediction of breeding values depends on the reliable estimation of variance components. This complex task leads to nonlinear minimization problems that have to be solved by numerical algorithms. In order to evaluate the reliability of these algorithms benchmark problems have to be constructed where the exact solution is a priori known. We develop techniques to construct such benchmark problems for mixed models including fixed and random effects, ANOVA, ML and REML predictors, balanced and unbalanced data for 1-way classification. Besides the construction of artificial data that produce the desired variance components we describe a projection method to construct benchmark data from simulated data. We discuss the cases where exact expressions for the projection can be given and where a numerical approximation procedure has to be used.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Scientific Computing, Technical University Dresden, 01062, Dresden, Germany

    Jörg Wensch

  2. Institute of Agricultural and Nutritional Sciences, Martin-Luther-University Halle-Wittenberg, 06099, Halle, Germany

    Monika Wensch-Dorendorf & Hermann H. Swalve

Authors
  1. Jörg Wensch
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  2. Monika Wensch-Dorendorf
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  3. Hermann H. Swalve
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Correspondence to Jörg Wensch.

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Wensch, J., Wensch-Dorendorf, M. & Swalve, H.H. The evaluation of variance component estimation software: generating benchmark problems by exact and approximate methods. Comput Stat 28, 1725–1748 (2013). https://doi.org/10.1007/s00180-012-0376-3

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  • DOI: https://doi.org/10.1007/s00180-012-0376-3

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