Fixed-α and fixed-β efficiencies

Christopher S. Withers; Saralees Nadarajah

ESAIM: Probability and Statistics (2013)

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

Abstract

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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.

How to cite

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Withers, 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 -

References

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