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Data Driven Rank Test for Two‐Sample Problem

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  • Alicja Janic‐Wró
  • Teresa Ledwina

Abstract

Traditional linear rank tests are known to possess low power for large spectrum of alternatives. In this paper we introduce a new rank test possessing a considerably larger range of sensitivity than linear rank tests. The new test statistic is a sum of squares of some linear rank statistics while the number of summands is chosen via a data‐based selection rule. Simulations show that the new test possesses high and stable power in situations when linear rank tests completely break down, while simultaneously it has almost the same power under alternatives which can be detected by standard linear rank tests. Our approach is illustrated by some practical examples. Theoretical support is given by deriving asymptotic null distribution of the test statistic and proving consistency of the new test under essentially any alternative.

Suggested Citation

  • Alicja Janic‐Wró & Teresa Ledwina, 2000. "Data Driven Rank Test for Two‐Sample Problem," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 281-297, June.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:2:p:281-297
    DOI: 10.1111/1467-9469.00189
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    Cited by:

    1. Axel Munk & Jean-Pierre Stockis & Janis Valeinis & Götz Giese, 2011. "Neyman smooth goodness-of-fit tests for the marginal distribution of dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 939-959, October.
    2. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    3. Cécile Durot & Piet Groeneboom & Hendrik P. Lopuhaä, 2013. "Testing equality of functions under monotonicity constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 939-970, December.

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