Abstract
A locally most powerful rank test (LMPRT) for the ordered scale alternatives is derived, assuming that the location parameters of the populations are all equal but unknown. A parametric test based on the likelihood derivative method is also obtained for the ordered scale alternatives. Asymptotic distributions of both the statistics are derived and the statistics are compared via the Pitman efficiency criterion. It is surmised that the asymptotic efficiency of the LMPRT relative to the likelihood derivative test procedure is less than one and tends to unity as the number of samples becomes large. A heuristic class of rank tests is also proposed for the above hypothesis-testing problem, where certain constants are chosen so as to maximize the efficacy. An asymptotically distribution-free test is also proposed for the case when the locations are unequal and unknown.
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References
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© 1978 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Govindarajulu, Z., Gupta, G.D. (1978). Tests for Homogeneity of Scale Against Ordered Alternatives. In: Transactions of the Eighth Prague Conference. Czechoslovak Academy of Sciences, vol 8A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9857-5_22
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DOI: https://doi.org/10.1007/978-94-009-9857-5_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9859-9
Online ISBN: 978-94-009-9857-5
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