# Fixed-α and fixed-β efficiencies

Christopher S. Withers; Saralees Nadarajah

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 224-235
- ISSN: 1292-8100

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topWithers, Christopher S., and Nadarajah, Saralees. "Fixed-α and fixed-β efficiencies." ESAIM: Probability and Statistics 17 (2013): 224-235. <http://eudml.org/doc/273617>.

@article{Withers2013,

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.},

author = {Withers, Christopher S., Nadarajah, Saralees},

journal = {ESAIM: Probability and Statistics},

keywords = {bahadur efficiency; fixed-α efficiency; fixed-β efficiency; goodness-of-fit tests; Hodges–Lehmann efficiency; Bahadur efficiency; fixed-$\alpha $ efficiency; fixed-$\beta $ efficiency; Hodges-Lehmann efficiency},

language = {eng},

pages = {224-235},

publisher = {EDP-Sciences},

title = {Fixed-α and fixed-β efficiencies},

url = {http://eudml.org/doc/273617},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Withers, Christopher S.

AU - Nadarajah, Saralees

TI - Fixed-α and fixed-β efficiencies

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 224

EP - 235

AB - 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.

LA - eng

KW - bahadur efficiency; fixed-α efficiency; fixed-β efficiency; goodness-of-fit tests; Hodges–Lehmann efficiency; Bahadur efficiency; fixed-$\alpha $ efficiency; fixed-$\beta $ efficiency; Hodges-Lehmann efficiency

UR - http://eudml.org/doc/273617

ER -

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