Geodesic
The multisample version of the Lepage test
Kybernetika, Tome 41 (2005) no. 6, pp. 713-733 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of $k>1$ sampled populations. It is shown that its limiting distribution is the chi-square distribution with $2(k-1)$ degrees of freedom. This $k$-sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular alternatives, the power of the $k$-sample test is compared with the power of the Kruskal–Wallis test or with the power of the Ansari–Bradley test by means of simulation estimates. Multiple comparison methods for detecting differing populations, based on this multisample version of the Lepage test or on the multisample version of the Ansari–Bradley test, are also constructed.
The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of $k>1$ sampled populations. It is shown that its limiting distribution is the chi-square distribution with $2(k-1)$ degrees of freedom. This $k$-sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular alternatives, the power of the $k$-sample test is compared with the power of the Kruskal–Wallis test or with the power of the Ansari–Bradley test by means of simulation estimates. Multiple comparison methods for detecting differing populations, based on this multisample version of the Lepage test or on the multisample version of the Ansari–Bradley test, are also constructed.
Classification : 62E20, 62G10, 62J15, 65C60
Keywords: multisample rank test for location and scale; Lepage statistic; consistency; non-centrality parameter; multiple comparisons for location and scale parameters 
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Rublík, František. The multisample version of the Lepage test. Kybernetika, Tome 41 (2005) no. 6, pp. 713-733. http://geodesic.mathdoc.fr/item/KYB_2005_41_6_a2/

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