Fixed-α and fixed-β efficiencies
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 224-235

Consider testing H0 : F ∈ ω0 against H1 : F ∈ ω1 for a random sample X1, ..., Xn from F, where ω0 and ω1 are two disjoint sets of cdfs on ℝ = (-∞, ∞). Two non-local types of efficiencies, referred to as the fixed-α and fixed-β efficiencies, are introduced for this two-hypothesis testing situation. Theoretical tools are developed to evaluate these efficiencies for some of the most usual goodness of fit tests (including the Kolmogorov-Smirnov tests). Numerical comparisons are provided using several examples.

DOI : 10.1051/ps/2011143
Classification : 62F03, 62F05, 62F12
Keywords: bahadur efficiency, fixed-α efficiency, fixed-β efficiency, goodness-of-fit tests, Hodges-Lehmann efficiency 
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Withers, Christopher S.; Nadarajah, Saralees. Fixed-$\alpha $ and fixed-$\beta $ efficiencies. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 224-235. doi: 10.1051/ps/2011143

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