Parametric bootstrap and approximate tests for two Poisson variates
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 alpha 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 alpha. We apply the tests to breast cancer data and injurious motor vehicle crash data.
parametric bootstrap asymptotic tests monte carlo tests poisson process rate ratio