The efficacy of some c-sample rank tests of homogeneity against ordered alternatives

Abstract

Reprinrs avrihbk d i d y from the pubtidm Photocopying pnnincd by t ionly 0 2000 OPA (OKnar PIlMirhm Alsociation) N.V. PuMirhad by liceme un&r the Gordon and B m c h Science h W m imprint. R i n d in Malaysia.For the c-sample location problem with ordered alternatives the test of Jonckhcm (1954) and Terpstra (1952) is a well-known competitor to the parametric test introduad by Barlow er al. (1972, p. 184). Generalizations of the Jonckhcen-Terpstra test are proposed e.g., by Puri (1%5), Tryoa and Hettmanspergcr (1973) and Biining and Kijssler (1996). All Lbcse test3 arc based on the painvise ranking method. In the present paper their efficacia are compared. The Jonckhem-type and Tryon-Hettmanspergertype t a t statistia can be further generalized by introducing weight coefficients to the substatistics For the case of a specified alternative these weights arc determined to obtain maximal efficacies. It is shown that the maximal achievable efficacies in the defined classes of generalized Jonckhcere-type tests and Tryon-Hettmansperger-type tests always are equal.

Somec-sample rank tests of homogeneity against umbrella alternatives with unknown peak

“…In most cases, the tests of Tryon-Hettmansperger-type are found to be worse than the other tests, especially in the case of unequal sample sizes. The Puri-type test is asymptotically equivalent to the MWT-test [5]. In simulations this test performed slightly worse than the CWT-test.…”

A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives

“…For = or = 1, the umbrella alternative corresponds to ordered alternative. For testing of ordered alternative, Jonckheere (1954) and Terpstra (1952) firstly proposed a test which is further modified by a number of researchers and references may be made to Amita and Kochar (1989), Kumar et al (1994 a, b), Büning and Kössler (1996), Kumar et al (2003), Kössler (2005), Goyal and Kumar (2017) and Kumar and Goyal (2018).…”

Using the Bernoulli trial approaches for detecting ordered alternatives

“…For instance, Puri [ 1 ], Puri and Sen [ 2 ], and Padmanabhan et al [ 3 ] applied the concept of Chernoff–Savage-type statistics to nonparametric ordered alternative tests. Studies that used power results to compare the validity of linear rank tests included Büning and Kössler [ 4 ], Beier and Büning [ 5 ], Büning and Kössler [ 6 ], Büning [ 7 ], Büning and Kössler [ 8 ], Büning and Kössler [ 9 ], Kössler [ 10 ] and Kössler [ 11 ].…”