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    A Random-Linear-Extension Test Based on Classic Nonparametric Procedures

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    Genre
    Thesis/Dissertation
    Date
    2009
    Author
    Cao, Jun
    Advisor
    Smith, Woollcott, 1941-
    Committee member
    Parnes, Milton
    Raghavarao, Damaraju
    Chitturi, Pallavi
    Rosenthal, Edward C., 1959-
    Department
    Statistics
    Subject
    Statistics
    Gibbs Sampler
    Linear Extension
    Nonparametric
    Partial Ordering
    Randomized Test
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/901
    
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    DOI
    http://dx.doi.org/10.34944/dspace/883
    Abstract
    Most distribution free nonparametric methods depend on the ranks or orderings of the individual observations. This dissertation develops methods for the situation when there is only partial information about the ranks available. A random-linear-extension exact test and an empirical version of the random-linear-extension test are proposed as a new way to compare groups of data with partial orders. The basic computation procedure is to generate all possible permutations constrained by the known partial order using a randomization method similar in nature to multiple imputation. This random-linear-extension test can be simply implemented using a Gibbs Sampler to generate a random sample of complete orderings. Given a complete ordering, standard nonparametric methods, such as the Wilcoxon rank-sum test, can be applied, and the corresponding test statistics and rejection regions can be calculated. As a direct result of our new method, a single p-value is replaced by a distribution of p-values. This is related to some recent work on Fuzzy P-values, which was introduced by Geyer and Meeden in Statistical Science in 2005. A special case is to compare two groups when only two objects can be compared at a time. Three matching schemes, random matching, ordered matching and reverse matching are introduced and compared between each other. The results described in this dissertation provide some surprising insights into the statistical information in partial orderings.
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