Goodness-of-fit: a comparison of parametric bootstrap and exact conditional tests.
A key point of any statistical analysis is verifying the assumptions made about the data. For example, is a normal distribution an adequate description for the data. This is often done using a goodness-of-fit test. There are many ways to conduct such test.
We study goodness of fit tests for exponential families. We compare, via Monte Carlo simulations, the powers of exact conditional tests based on co-sufficient samples (samples from the conditional distribution given the sufficient statistic) and approximate unconditional tests based on the parametric bootstrap. We use the Gibbs sampler to generate the co-sufficient samples. The gamma and von Mises families are investigated, and the Cramer-von Mises and Watson test statistics are applied. The results of this study show that those two tests have very similar powers even for samples of very small size, such as n=5.
This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact Wei Qian (firstname.lastname@example.org) or his supervisor Richard Lockhart (email@example.com), Department of Statistics and Actuarial Science.