Characterization of non-linear profiles variations using mixed-effect models and wavelets

There is an increasing research interest in the modeling and analysis of complex non-linear profiles using the wavelet transform. However, most existing modeling and analysis methods assume that the total inherent profile variations are mainly due to the noise within each profile. In many practical situations, however, the profile-to-profile variation is often too large to be neglected. In this article, a new method is proposed to model non-linear profile data variations using wavelets. For this purpose, a wavelet-based mixed-effect model is developed to consider both within- and between-profile variations. The utilization of wavelets not only simplifies the computational complexity of the mixed-effect model estimation but also facilitates the identification of the sources of the between-profile variations. In addition, a change-point model involving the likelihood ratio test is applied to ensure that the collected profiles used in the model estimation follow an identical distribution. Finally, the performance of the proposed model is evaluated using both Monte Carlo simulations and a case study.