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Kössler, Wolfgang

Some \(c\)-sample rank tests of homogeneity against ordered alternatives based on U-statistics. (English) Zbl 1117.62044

J. Nonparametric Stat. 17, No. 7, 777-795 (2005).
Summary: For the \(c\)-sample location problem with ordered alternatives we construct some test statistics, all of them are based on U-statistics. Several statistics from the literature are generalized and extended to our problem. In particular, the statistics of J. Xie and C. E. Priebe [J. Stat. Plann. Inference 102, No. 2, 441–466 (2002; Zbl 0989.62027)] are generalized from the two-sample problem. All the corresponding tests are based on different pairwise ranking methods, that of M. L. Puri [Commun. Pure Appl. Math. 18, 51–63 (1965; Zbl 0135.19602)], of P. V. Tryon and T. P. Hettmansperger [Ann. Stat. 1, 1061–1070 (1973; Zbl 0275.62041)], and of H. Büning and W. Kössler [J. Stat. Comput. Simulation 55, No. 4, 337–352 (1996; Zbl 0874.62012)]. The asymptotic power and the asymptotic relative efficiency are derived. Some of these tests are used to construct adaptive tests. A simulation study shows that the asymptotic results can be used for sample sizes as small as \(n_i = 10\).

Cited in 8 Documents

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62F30 Parametric inference under constraints

Keywords:

Jonckheere-type test; Puri-type test; Tryon-Hettmansperger-type test; adaptive test; efficacy; asymptotic relative efficiency

Citations:

Zbl 0989.62027; Zbl 0874.62012; Zbl 0135.19602; Zbl 0275.62041
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