On the Residual Plot in a Mixture Model

The residual plot is a graphical diagnostic that can tell whether a mixture model is necessary. We establish the approximate joint normality of the residual function nonparametrically. We propose an approach to constructing simultaneous asymptotic confidence bands. Our investigation is extended to the empirical log-ratio plot to obtain better visual effect sometimes. The type I error rate is under control to some degree in the proposed procedures with confidence bands based on nonparametric estimation. The proposed procedures are adopted in proteomic and ecological applications. It is found that the probabilities being detected on gels vary over proteins, and that there is no evidence for beetles to be removed with different probabilities.