Likelihood-Based Confidence Intervals for Complementary Poisson Rate Parameters with Misclassified Data

Abstract

We derive three interval estimators for complementary Poisson rates where the data are possibly misclassified: a Wald-based interval, a score-based interval, and an interval based on the profile log-likelihood statistic. Also, we derive an EM algorithm to determine profile maximum likelihood estimators. We investigate the coverage and average width properties of these intervals via a simulation study. The Wald interval is generally the narrowest, but can have some coverage problems when the Poisson counts are small. Lastly, we apply the newly derived confidence intervals to a real data set involving traffic accident data that contains misclassified counts.