Open Access
December, 1965 Alternative Efficiencies for Signed Rank Tests
Jerome Klotz
Ann. Math. Statist. 36(6): 1759-1766 (December, 1965). DOI: 10.1214/aoms/1177699804


Asymptotic efficiency curves for the one sample Wilcoxon and normal scores tests are obtained by comparing the exponential rate of convergence to zero of the type I error $(\alpha)$ while keeping the type II error $(\beta)$ fixed $(0 < \beta < 1)$. A wider than usual view of test performance consistent with small sample results is obtained. The Pitman efficiency value is derived as a special case when the alternative approaches the null hypothesis. Comparisons of the signed rank tests relative to $\bar{x}$ or $t$ for normal location alternatives yield small efficiency values for extreme alternatives. The relative performance of the Wilcoxon is seen to be slightly better than the normal scores for normal alternatives with larger location parameter values despite the local (Pitman) optimality of the normal scores. Similar results hold for two other non-normal alternatives considered.


Download Citation

Jerome Klotz. "Alternative Efficiencies for Signed Rank Tests." Ann. Math. Statist. 36 (6) 1759 - 1766, December, 1965.


Published: December, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0151.23604
MathSciNet: MR185760
Digital Object Identifier: 10.1214/aoms/1177699804

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 6 • December, 1965
Back to Top