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Contributions to generalized Wilcoxon rank tests
Umeå University, Faculty of Social Sciences, Department of Statistics.
1992 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In unbalanced small sample size problems with right censorings, the variance estmators of linear rank statistics, may be biased. This is the case with the commonly applied variance estimators for the generalized Wilcoxon rank test statistics of Gehan and Prentice. The bias and variance of different variance estimators and observed significance level and power for standardized tests are compared in a Monte Carlo simulation study. The variance estimators are the permutational-, the conditional permutational- and the jackknife variance estimators for the statistic Gehan, and the asymptotic- and the jackknife variance estimators for the statistic of Prentice. It appears that observed level and power and variance properties may be improved by using the jackknife variance estimator.

Further, The sensitivity curves of Turkey are used to establish the sensitivity to gross errors and misclassifications for standardized generalized Wilcoxon rank sum statistics in small samples with right censorings. For a certain combined sample, which might contain gross errors, a relatively fast method is needed to establish the applicability of the inference drawn from the selected ranktest. Ome way is to use the "change of decision point" (cdp), which in this thesis is defined as the smallest proportion of altered positions resulting in an opposite decision.

Place, publisher, year, edition, pages
Umeå: Department of Statistics, University of Umeå , 1992. , 30 p.
Series
Statistical studies, ISSN 1100-8989 ; 18
Keyword [en]
Censored data rank sum tests, Gehan's test, Generalized Wilcoxon test, Jackknifing, Two sample problem, Simulation, Survival data, Variance estimation, Influence function, Gross error sensitivity, Sensitivity curve, Misclassification
National Category
Computer and Information Science
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-7286ISBN: 91-7174-655-2 (print)OAI: oai:DiVA.org:umu-7286DiVA: diva2:146957
Presentation
, Umeå universitet, Umeå (English)
Opponent
Supervisors
Available from: 2007-02-12 Created: 2007-02-12 Last updated: 2010-03-10Bibliographically approved
List of papers
1. A Monte Carlo study of some censored data Wilcoxon rank tests
Open this publication in new window or tab >>A Monte Carlo study of some censored data Wilcoxon rank tests
1990 (English)In: Biometrical Journal, ISSN 0323-3847, Vol. 32, no 6, 721-735 p.Article in journal (Refereed) Published
Abstract [en]

The variance estimators usually applied for the generalized censored data Wilcoxon rank tests by Gehan and Peto & Prentice, are heavily biased in unbalanced problems. This paper reports the results of a Monte Carlo simulation study, where jackknifing is used to construct estimators of variance. Size, power and variance properties are compared for five variance estimators, when using different combinations of group sizes, failure and censoring patterns. The variance estimators are the permutational, the conditional permutational and the jackknife variance estimators for the statistic of Gehan and the asymptotic and the jackknife variance estimators for the statistic of Peto & Prentice. It appears that observed size, power and variance properties may be improved by using the jackknife variance estimator, when comparing to the variance estimators usually applied.

Place, publisher, year, edition, pages
Weinheim, Germany: WILEY-VCH Verlag GmbH & Co. KGaA, 1990
Keyword
Censored data rank tests, Gehan's test, Generalized Wilcoxon test, Jackknifing, Two sample problem, Simulation, Survival data, Variance estimation
National Category
Computer and Information Science
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-32355 (URN)10.1002/bimj.4710320612 (DOI)
Available from: 2010-03-10 Created: 2010-03-10 Last updated: 2010-03-10Bibliographically approved
2. Generalized Wilcoxon rank tests and sensitivity curves
Open this publication in new window or tab >>Generalized Wilcoxon rank tests and sensitivity curves
1991 (English)In: Biometrical Journal, ISSN 0323-3847, Vol. 33, no 7, 789-806 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we use the sensitivity curves of TUKEY (1977) and the change of decision point (cdp) (a modified version of the breakdown point of YLVISAKER, 1977), supplemented by simulation studies to acquire knowledge about sensitivity in generalized Wilcoxon rank test statistics. Sensitivity depends on balanced or unbalanced sample size cases, censoring, combinations of failure distributions and sources of errors in the data. It is important to consider the quality of the data, and the results show that cdp and some properties of the sensitivity curves may serve as a hint when selecting a test statistic and when making a decision for a given test statistic.

Place, publisher, year, edition, pages
Weinheim, Germany: WILEY-VCH Verlag GmbH & Co. KGaA, 1991
Keyword
Censored data rank tests, Gehan's test, Generalized Wilcoxon test, Jackknifing, Two sample problem, Simulation, Survival data, Variance estimation, Influence function, Gross error sensitivity, Break down point, Sensitivity curve
National Category
Computer and Information Science
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-32354 (URN)10.1002/bimj.4710330706 (DOI)
Available from: 2010-03-10 Created: 2010-03-10 Last updated: 2010-03-10Bibliographically approved

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Öhman, Marie-Louise

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