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Yi Li Dissertation.pdf (860.11 KB)

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Goodness-of-Fit Tests For Dirichlet Distributions With Applications

Li, Yi
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1435003723

Abstract Details

2015, Doctor of Philosophy (Ph.D.), Bowling Green State University, Statistics.
ABSTRACT Maria Rizzo, Advisor We present five new goodness-of-fit tests for Dirichlet distributions. Since beta, Dirichlet, and generalized Dirichlet distributions are widely used in statistics such as Dirichlet regression, data mining, and machine learning. Thus, goodness-of-fit tests for beta and Dirichlet distribution are important applications. We develop new test procedures for testing beta and Dirichlet distribution. The first test, called energy test, is based on energy statistics. The second test, called distance covariance test, is based on the property of complete neutrality of the Dirichlet distribution and distance covariance tests. We also expand the distance covariance test into testing the mutual in- dependence of all components of arbitrary random vector. The third, fourth and fifth tests, called the triangle tests, are based on the interpoint distances. Simulation studies of power performance for the new beta and Dirichlet goodness-of-fit tests are presented. Results show that distance co- variance goodness-of-fit test have good performance in contaminated Dirichlet distributions which contain the small perturbation in the Dirichlet distribution. The parameter estimation based on the maximum likelihood is derived for the generalized Dirichlet distribution and the initial value for the iteration of the Newton-Raphson algorithm is also proposed. Applications includes the goodness-of-fit tests of Dirichlet and generalized Dirich- let distributions, model evaluation of Dirichlet regression models, and influence diagnostics of Dirichlet regression models.
Maria Rizzo (Advisor)
Pamela Bechtel (Committee Member)
James Albert (Committee Member)
Wei Ning (Committee Member)
91 p.
Statistics
testing mutual independence of a collection of random variables, random vectors, or random samples; Goodness-of-fit tests; standardized transformation for Dirichlet; Dirichlet Distribution; generalized Dirichlet distribution; Dirichlet regression

Recommended Citations

Citations

  • Li, Y. (2015). Goodness-of-Fit Tests For Dirichlet Distributions With Applications [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1435003723

    APA Style (7th edition)

  • Li, Yi. Goodness-of-Fit Tests For Dirichlet Distributions With Applications. 2015. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1435003723.

    MLA Style (8th edition)

  • Li, Yi. "Goodness-of-Fit Tests For Dirichlet Distributions With Applications." Doctoral dissertation, Bowling Green State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1435003723

    Chicago Manual of Style (17th edition)

bgsu1435003723
3,678
© 2015, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.