Estimating change in a proportion by combining measurements from a true and a fallible classifier

Abstract

Consider a binary classification of a large population at two points in time. The classification is observed with error for the whole population using a fallible classifier and without error for a random sample using an accurate classifier. Following Tenenbein (1970), the population proportions are estimated by poststratification according to the fallible classifier for both the time points. Assuming a multinomial probability model, the joint asymptotic normality of the two estimators is demonstrated. Comparison is made with the estimator based on the survey data only. In particular the importance of including the same items in the samples at both time points is discussed.