Estimation from binomial data with classifiers of known and unknown imperfections

Observations from inspection by a ‘test’ method and a standard method are combined to provide estimators of population proportion, and of probabilities of misclassification for the test method. Results of Hochberg and Tenenbein and of Albers and Veldman are extended to the case where the standard method is not perfect, but its misclassification probabilities have known values. Both moment and maximum-likelihood estimators are considered and some asymptotic properties of the resulting estimators are compared.