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Fixed-α and fixed-β efficiencies

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. saralees.nadarajah@manchester.ac.uk
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Abstract

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.

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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