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

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 w...

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Bibliographic Details
Published in:Computational statistics 2013-08, Vol.28 (4), p.1725-1748
Main Authors: Wensch, Jörg, Wensch-Dorendorf, Monika, Swalve, Hermann H.
Format: Article
Language:English
Subjects:
Algorithms
Analysis of variance
Approximation
Benchmarking
Construction
Economic Theory/Quantitative Economics/Mathematical Methods
Estimating techniques
Mathematical analysis
Mathematical models
Mathematics and Statistics
Original Paper
Parameter estimation
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Projection
Random variables
Software
Statistics
Studies
Variance
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Summary: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.
ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-012-0376-3