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fixed-β efficiency

ESAIM: Probability and Statistics (1)

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Fixed-α and fixed-βefficiencies
Christopher S. Withers, Saralees Nadarajah
Journal:

ESAIM: Probability and Statistics / Volume 17 / 2013

Published online by Cambridge University Press:

08 February 2013, pp. 224-235

Print publication:

2013
- Article
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Consider testingH0 : F ∈ ω0against H1 : F ∈ ω1for a random sampleX1, ..., Xnfrom F, where ω0 andω1 are two disjoint sets of cdfs onℝ = (−∞, ∞). Two non-local types of efficiencies, referred to as thefixed-α and fixed-β efficiencies, are introduced forthis two-hypothesis testing situation. Theoretical tools are developed to evaluate theseefficiencies for some of the most usual goodness of fit tests (including theKolmogorov–Smirnov tests). Numerical comparisons are provided using several examples.