Data driven rank tests for classes of tail alternatives

Willem Albers, Wilbert C.M. Kallenberg, Felix Martini

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Abstract

Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages26
Publication statusPublished - 1999

Publication series

Name
PublisherDepartment of Applied Mathematics, University of Twente
No.1504
ISSN (Print)0169-2690

Keywords

  • MSC-62E25
  • MSC-62G10
  • MSC-62G20

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