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Asympotic efficiency of signed - rank symmetry tests under skew alternatives

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  • Alessandra Durio
  • Yakov Nikitin

Abstract

The efficiency of some known tests for symmetry such as the sign test, the Wilcoxon signed-rank test or more general linear signed rank tests was studied mainly under the classical alternatives of location. However it is interesting to compare the efficiencies of these tests under asymmetric alternatives like the so-called skew alternative proposed in Azzalini (1985). We find and compare local Bahadur efficiencies of linear signed-rank statistics for skew alternatives and discuss also the conditions of their local optimality. We calculate also such efficiencies for the family of distribution-free Maesono statistics proposed in Maesono (1987).

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers with number 12-2002.

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Length: 14 pages
Date of creation: Feb 2002
Date of revision:
Handle: RePEc:icr:wpicer:12-2002

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Keywords: skew family; linear rank test; Maesono statistic; Bahadur efficiency; local optimality;

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  1. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods and Applications, Springer, vol. 7(1), pages 1-13, April.
  2. E. Kremer, 1982. "Local comparison of linear rank tests, in the Bahadur sense," Metrika, Springer, vol. 29(1), pages 159-173, December.
  3. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
  4. Ya. Nikitin & E. Ponikarov, 2002. "Asymptotic Efficiency of Maesono Statistics for Testing of Symmetry," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 382-390, June.
  5. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
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