Quasi Most Powerful Invariant Tests of Goodness-of-Fit

doi:https://doi.org/10.1007/978-1-4612-0103-8_26

Book Chapter10.1007/978-1-4612-0103-8_26

Quasi Most Powerful Invariant Tests of Goodness-of-Fit

Gilles R. Ducharme,Benoît Frichot-2002-01-01-Birkhäuser Boston eBooks

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TL;DRAbstract

In this chapter, we consider the problem of testing the goodness-offit of either one of two location-scale families of density when these parameters are unknown. We derive anO(n -1 )approximation to the densities of the maximal invariant on which the most powerful invariant test is based. The resulting test, which we call quasi most powerful invariant, can be applied to many situations. The power of the new procedure is studied for some particular cases.

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In this chapter, we consider the problem of testing the goodness-offit of either one of two location-scale families of density when these parameters are unknown. We derive anO(n -1 )approximation to the densities of the maximal invariant on which the most powerful invariant test is based. The resulting test, which we call quasi most powerful invariant, can be applied to many situations. The power of the new procedure is studied for some particular cases.

Keywords

Goodness of fitInvariant (physics)Scale invarianceMathematicsApplied mathematicsPure mathematicsDiscrete mathematicsStatistics

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