Functional Data Models for Raman Spectral Data and Degradation Analysis

Functional data analysis (FDA) studies data in the form of measurements over a domain as whole entities. Our first focus is on the post-hoc analysis with pairwise and contrast comparisons of the popular functional ANOVA model comparing groups of functional data. Existing contrast tests assume independent functional observations within group. In reality, this assumption may not be satisfactory since functional data are often collected continually overtime on a subject. In this work, we introduce a new linear contrast test that accounts for time dependency among functional group members. For a significant contrast test, it can be beneficial to identify the region of significant difference. In the second part, we propose a non-parametric regression procedure to obtain a locally sparse estimate of functional contrast. Our work is motivated by a biomedical study using Raman spectroscopy to monitor hemodialysis treatment near real-time. With contrast test and sparse estimation, practitioners can monitor the progress of the hemodialysis within session and identify important chemicals for dialysis adequacy monitoring. In the third part, we propose a functional data model for degradation analysis of functional data. Motivated by degradation analysis application of rechargeable Li-ion batteries, we combine state-of-the-art functional linear models to produce fully functional prediction for curves on heterogenous domains. Simulation studies and data analysis demonstrate the advantage of the proposed method in predicting degradation measure than existing method using aggregation method.