A revisit to testing the equality of several Poisson parameters

Recently Chang et al. [4] considered testing the equality of several Poisson parameters, and proposed a new parametric bootstrap (PB) method, called 'CAT'. The CAT was compared against fourteen other tests including the 'asymptotic likelihood ratio test' (ALRT) as well as the PB version of the likelihood ratio test (henceforth, PBLRT), and all were found to be conservative unless the common parameter values under the null hypothesis were not too small. In this paper we have proposed a few new test procedures based on two broad adjustments, namely (i) using different 'metrics' which measure deviation of the model parameters from the null hypothesis; and (ii) using shrinkage estimators in the aforementioned 'metrics'. All the new tests are PB in nature which obtain their respective critical values through computational steps (i.e., one does not need to know the critical values explicitly for these tests). The resultant new tests are then studied through a comprehensive simulation, and compared against ALRT and PBLRT in terms of size and power. It has been noted that while two analogous versions of PBLRT work similar to PBLRT for small to moderate sample sizes, they tend to be almost identical for large sample sizes. Therefore, based on the overall performance we recommend PBLRT always.