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Fixed-α and fixed-βefficiencies

Published online by Cambridge University Press:  08 February 2013

Christopher S. Withers  and
Saralees Nadarajah
Christopher S. Withers
Affiliation:
Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand
Saralees Nadarajah
Affiliation:
School of Mathematics, University of Manchester, M13 9PL Manchester, UK. [email protected]
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Abstract

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.

Keywords

Bahadur efficiencyfixed-α efficiencyfixed-β efficiencygoodness-of-fit testsHodges–Lehmann efficiency
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 224 - 235
Copyright
© EDP Sciences, SMAI, 2013

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