Maximum Likelihood Estimation of Two Inversely Related Poisson Rate Parameters with Misclassified Data

SYNOPTIC ABSTRACT

We derive maximum likelihood estimators (MLEs) for two inversely related Poisson rate parameters when data is subject to misclassification. We assume a cheap error-prone device is used to search a large area and an expensive error-free search method is utilized on a smaller area. This double sample allows identification of all unknown parameters. Additionally, we derive large sample variance approximations for the rate parameter estimators, give asymptotic confidence intervals for the rate parameters, and study these confidence intervals via a Monte Carlo simulation. We then apply the newly derived estimator and confidence intervals to a real data problem.

Key Words and Phrases:

• Under-reporting
• over-reporting
• Fisher Information matrix
• delta method of variance approximation