Detecting positive quadrant dependence and positive function dependence

A. Janic-Wróblewska, W.C.M. Kallenberg, T. Ledwina

Research output: Book/ReportReportProfessional

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Abstract

There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty of Mathematical Sciences
Number of pages27
Publication statusPublished - 2003

Publication series

NameMemorandum Faculty of Mathematical Sciences
PublisherDepartment of Applied Mathematics, University of Twente
No.1689
ISSN (Print)0169-2690

Keywords

  • MSC-62G10
  • MSC-62H20
  • IR-65874
  • EWI-3509
  • METIS-213197
  • MSC-65C05

Cite this

Janic-Wróblewska, A., Kallenberg, W. C. M., & Ledwina, T. (2003). Detecting positive quadrant dependence and positive function dependence. (Memorandum Faculty of Mathematical Sciences; No. 1689). Enschede: University of Twente, Faculty of Mathematical Sciences.
Janic-Wróblewska, A. ; Kallenberg, W.C.M. ; Ledwina, T. / Detecting positive quadrant dependence and positive function dependence. Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; 1689).
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Janic-Wróblewska, A, Kallenberg, WCM & Ledwina, T 2003, Detecting positive quadrant dependence and positive function dependence. Memorandum Faculty of Mathematical Sciences, no. 1689, University of Twente, Faculty of Mathematical Sciences, Enschede.

Detecting positive quadrant dependence and positive function dependence. / Janic-Wróblewska, A.; Kallenberg, W.C.M.; Ledwina, T.

Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; No. 1689).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Detecting positive quadrant dependence and positive function dependence

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N2 - There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.

AB - There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.

KW - MSC-62G10

KW - MSC-62H20

KW - IR-65874

KW - EWI-3509

KW - METIS-213197

KW - MSC-65C05

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BT - Detecting positive quadrant dependence and positive function dependence

PB - University of Twente, Faculty of Mathematical Sciences

CY - Enschede

ER -

Janic-Wróblewska A, Kallenberg WCM, Ledwina T. Detecting positive quadrant dependence and positive function dependence. Enschede: University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; 1689).