Inferences in dichotomous classifications with misclassifications based on sequential repetitive classifications

ABSTRACT To create inferences in dichotomous classifications with misclassifications and possibly perform repeated classifications, the maximum likelihood method is commonly used, mainly because of its efficiency in obtaining parameter estimators of a mixture of two binomial distributions. One simpler alternative that is operationally easier is to consider the simple majority method. In this method, each of n items are classified r times as conforming or non-conforming. The final classification of the item is determined by the most frequent class. This method yielded lower mean squared errors than the maximum likelihood and the moments estimators and is asymptotically efficient. In this paper, we introduce a new approach in which the realization of all r repeated classifications of each item may not be needed. Each of n items is sequentially classified as conforming or nonconforming, and the process ceases when the frequency of conforming or non-conforming classification reaches the integer a. We show that, by a Monte Carlo simulation, the last procedure presents a lower mean squared error than the simple majority results for a similar number of r repeated classifications.