Inference for the K-sample problem based on precedence probabilities

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Show simple item record Dey, Rajarshi 2011-08-11T15:22:11Z 2011-08-11T15:22:11Z 2011-08-11
dc.description.abstract Rank based inference using independent random samples to compare K>1 continuous distributions, called the K-sample problem, based on precedence probabilities is developed and explored. There are many parametric and nonparametric approaches, most dealing with hypothesis testing, to this important, classical problem. Most existing tests are designed to detect differences among the location parameters of different distributions. Best known and most widely used of these is the F- test, which assumes normality. A comparable nonparametric test was developed by Kruskal and Wallis (1952). When dealing with location-scale families of distributions, both of these tests can perform poorly if the differences among the distributions are among their scale parameters and not in their location parameters. Overall, existing tests are not effective in detecting changes in both location and scale. In this dissertation, I propose a new class of rank-based, asymptotically distribution- free tests that are effective in detecting changes in both location and scale based on precedence probabilities. Let X_{i} be a random variable with distribution function F_{i} ; Also, let _pi_ be the set of all permutations of the numbers (1,2,...,K) . Then P(X_{i_{1}}<...<X_{i_{K}}) is a precedence probability if (i_{1},...,i_{K}) belongs to _pi_. Properties of these of tests are developed using the theory of U-statistics (Hoeffding, 1948). Some of these new tests are related to volumes under ROC (Receiver Operating Characteristic) surfaces, which are of particular interest in clinical trials whose goal is to use a score to separate subjects into diagnostic groups. Motivated by this goal, I propose three new index measures of the separation or similarity among two or more distributions. These indices may be used as “effect sizes”. In a related problem, Properties of precedence probabilities are obtained and a bootstrap algorithm is used to estimate an interval for them. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Precedence probabilities en_US
dc.subject Nonlinear rank-based statistic en_US
dc.subject U-statistic en_US
dc.subject K-sample problem en_US
dc.subject Index measures of distance among distributions en_US
dc.subject Hypervolume under ROC manifold en_US
dc.title Inference for the K-sample problem based on precedence probabilities en_US
dc.type Dissertation en_US Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Statistics en_US
dc.description.advisor Paul I. Nelson en_US
dc.subject.umi Statistics (0463) en_US 2012 en_US August en_US

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