Department of Mathematics
The parametric bootstrap tests and the asymptotic or approximate tests for detecting difference of two Poisson means are compared. The test statistics used are the Wald statistics with and without log-transformation, the Cox F statistic and the likelihood ratio statistic. It is found that the type I error rate of an asymptotic/approximate test may deviate too much from the nominal significance level α under some situations. It is recommended that we should use the parametric bootstrap tests, under which the four test statistics are similarly powerful and their type I error rates are all close to α. We apply the tests to breast cancer data and injurious motor vehicle crash data.
asymptotic tests, Monte Carlo tests, parametric bootstrap, Poisson process, rate ratio
Source Publication Title
Journal of Statistical Computation and Simulation
Taylor & Francis
Link to Publisher's Edition
Chiu, S. (2010). Parametric bootstrap and approximate tests for two Poisson variates. Journal of Statistical Computation and Simulation, 80 (3). https://doi.org/10.1080/00949650802609475