The most efficient linear combination of the Sign and the Maesono tests for p-normal distributions
DOI:
https://doi.org/10.6092/issn.1973-2201/3623Abstract
This paper deals with the Pitman most efficient Gr linear combination of the Sign and the Maesono tests for parent distributions belonging to the p-normal family of densities.
The most efficient linear combinations G2 and G4 are obtained. It is also shown that G2 (for leptokurtic p-normal distributions) and G4 (for platikurtic p-normal distributions) are much more efficient than Student’s t, with a maximum loss of efficiency of about 3,1% in the near proximity of the normal distribution (p=2).
References
G. BURGIO, YA. YU. NIKITIN (2001), The combination of the Sign and Wilcoxon tests for symmetry and their Pitman efficiency, “Asymptotic Methods in Probability and Mathematical Statistics”, 42, pp. 12-34.
G. BURGIO, YA. YU. NIKITIN (2003), On the combination of the Sign and Maesono tests for symmetry and its efficiency, “Statistica”, 63, 2, pp. 213-222.
J. HODGES AND E. LEHMANN (1956), The efficiency of some non parametric competitors of the t-test, “Annals of Mathematical Statistics”, 27, pp. 324-335.
W. HOEFFDING (1948), A class of statistics with asymptotically normal distributions, “Annals of Mathematical Statistics”, 19, pp. 293-325.
Y. MAESONO (1987), Competitors of the Wilcoxon signed rank test, “Annals of the Institute of Statistical Mathematics”, 39, Pt A, pp. 363-375.
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