### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1999 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1504 |

ISSN (Print) | 0169-2690 |

### Keywords

- IR-65692
- MSC-62E25
- MSC-62G10
- MSC-62G20
- EWI-3324

### Cite this

*Data driven rank tests for classes of tail alternatives*. Enschede: University of Twente, Department of Applied Mathematics.

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*Data driven rank tests for classes of tail alternatives*. University of Twente, Department of Applied Mathematics, Enschede.

**Data driven rank tests for classes of tail alternatives.** / Albers, Willem/Wim; Kallenberg, W.C.M.; Martini, F.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Data driven rank tests for classes of tail alternatives

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

AU - Martini, F.

N1 - Imported from MEMORANDA

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - IR-65692

KW - MSC-62E25

KW - MSC-62G10

KW - MSC-62G20

KW - EWI-3324

M3 - Report

BT - Data driven rank tests for classes of tail alternatives

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -