Fixed-$\alpha$ and fixed-$\beta$ efficiencies

Withers, Christopher S.; Nadarajah, Saralees

ESAIM: Probability and Statistics, Tome 17 (2013), pp. 224-235.

Consider testing H₀ : F ∈ ω₀ against H₁ : F ∈ ω₁ for a random sample X₁, ..., X_n 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.

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