Maximum Likelihood Estimation for a Binomial Parameter Using Double Sampling with one Type of Misclassification

SYNOPTIC ABSTRACT

A Maximum Likelihood Estimator (MLE) approach is considered for the estimation of a binomial proportion parameter in doubly sampled data subject to false positive misclassification. We assume that an inexpensive, error-prone device is used on a large main study and an expensive, error-free device is utilized on a smaller substudy. This double sample allows identifiability of all unknown parameters, because by incorporating additional information (data) via double sampling, the dimension of sufficient statistics is greater than or equal to the numbers of parameters; hence, the model becomes identifiable. Additionally, we derive two confidence intervals (CIs): a naïve Wald CI and a modified Wald CI, and we compare the performance of these two CIs in terms of coverage probability and average length, via a Monte Carlo simulation. We then apply the two newly derived estimator and confidence intervals to a real data problem.

Key Words and Phrases::

• false positive
• double sampling
• misclassification
• binary data

Acknowledgment

The authors thank the anonymous referees and the editor for their constructive comments and suggestions, which helped strengthen the manuscript.