Goodness of fit tests with misclassified data

The most popular goodness of fit test for a multinomial distribution is the chi-square test. But this test is generally biased if observations are subject to misclassification. In this paper we shall discuss how to define a new test procedure when we have double sample data obtained from the true and fallible devices. An adjusted chi-square test based on the imputation method and the likelihood ratio test are considered. Asymptotically, these two procedures are equivalent. However, an example and simulation results show that the former procedure is not only computationally simpler but also more powerful under finite sample situations.