Volume 17, 2013
|Page(s)||224 - 235|
|Published online||08 February 2013|
Fixed-α and fixed-β efficiencies
Applied Mathematics Group, Industrial Research
Limited, Lower Hutt,
2 School of Mathematics, University of Manchester, M13 9 PL Manchester, UK
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.
Mathematics Subject Classification: 62F03 / 62F05 / 62F12
Key words: Bahadur efficiency / fixed-α efficiency / fixed-β efficiency / goodness-of-fit tests / Hodges–Lehmann efficiency
© EDP Sciences, SMAI, 2013
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