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Intensive Numerical and Symbolic Computing in Parametric Test Theory

  • Dirk Wauters
  • Lea Vermeire
Conference paper
Part of the Statistics and Computing book series (SCO)

Abstract

In the construction of multiparameter significance tests intensive computing may be involved at two levels: numerical computing in the construction of critical regions with particular optimality properties, symbolic computing to obtain a better understanding of a statistical model e.g. by giving the geometry of the model. Each level is explained in the construction of two tests for a simple null hypothesis in two lifetime models.

The g-LMMPUMα test maximizes the local mean power with respect to a metric g under all unbiased tests. This test is obtained for the two-parameter gamma family. The construction of the critical region involves the solution of a system of non-linear equations, two-dimensional numerical quadrature, numerical Fourier inversion and interpolation. The NAG Fortran library is a basic tool.

The geodesic test uses the Rao distance (information distance) between the ML-estimators and the null hypothesis as test statistic. This test is obtained for the two-parameter Weibull family. The symbolic computation of tensor components and connection symbols requires essentially the partial derivatives of the loglikelihood and expectations. The Mathematica language allows direct symbolic computation of partial derivatives. For the expectations a package within Mathematica is constructed.

Key Words

gamma family geodesic test locally most mean power test Weibull family. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Dirk Wauters
    • 1
  • Lea Vermeire
    • 1
  1. 1.Katholieke Universiteit Leuven Campus KortrijkUniversitaire CampusKortrijkBelgium

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