INFERENCE ABOUT THE MEAN OF A POISSON DISTRIBUTION IN THE PRESENCE OF A NUISANCE PARAMETER

In this note we examine the problem of estimating the mean of a Poisson distribution when a nuisance parameter is present. Using a condition of Cox (1958) about ancillarity in the presence of a nuisance parameter, we justify that inference about the parameter should be carried out using the conditional distribution given the appropriate ancillary statistics. A small simulation study has been done to compare the performance of the conditional likelihood approach and the standard likelihood approach.