Mathematics Ph.D. Dissertations
Goodness-of-Fit Tests For Dirichlet Distributions With Applications
Date of Award
Doctor of Philosophy (Ph.D.)
Maria Rizzo (Advisor)
Pamela Bechtel (Committee Member)
James Albert (Committee Member)
Wei Ning (Committee Member)
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 Dirichlet distributions, model evaluation of Dirichlet regression models, and influence diagnostics of Dirichlet regression models.
Li, Yi, "Goodness-of-Fit Tests For Dirichlet Distributions With Applications" (2015). Mathematics Ph.D. Dissertations. 26.