Divergence-based estimation and testing with misclassified data

Abstract

The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and phi-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum phi-divergence estimators are considered and some of their properties are established. The proposed phi-divergence test statistics are obtained by calculating phi-divergences between probability density functions and by replacing parameters by their minimum phi-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example