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Title: Statistical inference for measures of stochastic ordering in comparative studies
Keywords: extended logistic family; boundary-respecting confidence interval; Mann-Whitney measure;Mann-Whitney statistic; stochastic ordering; ROC analysis
Issue Date: 8-Feb-2008
Citation: ZHAO YUDONG (2008-02-08). Statistical inference for measures of stochastic ordering in comparative studies. ScholarBank@NUS Repository.
Abstract: A simple semi-parametric method is introduced for constructing boundary-respecting confidence intervals for the two-sample Mann-Whitney measure.We show that stochastic ordering is equivalent to monotone transformation of location shift. Then consideration of a number of location shift families indicates a suitable class of shapes to model the asymptotic variance, leading to a confidence interval method based on roots of quadratics. This proposed scheme is also adapted to paired data. We show that a stochastically positive random variable and its negative can be transformed to a symmetric location shift model. We further give a central place to the logistic location shift model in the boundary-respecting interval procedure through a variance-controlling transformation, simplifying the calculations. We also generalize a distribution family from the logistic distribution, thus covering a wide range of symmetric distribution shapes. Based on this extended logistic family, we develop rank procedures which can always retain high efficiency for one-sample location problems.
Appears in Collections:Ph.D Theses (Open)

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