Colloquium: Dr. Ruiyan Luo

Speaker: Dr. Ruiyan Luo, Georgia State University

Title: Function-on-function regression for highly densely observed spiky functional data

Abstract: Modern technique allows data to be recorded with high sample rate, which leads to highly densely observed spiky curves. For example, the mass spectrometry data contains a number of narrow and high peaks which are interests of scientists, and the EEG curves exhibit high local variations over the whole time interval. The existing methods for function-on-function regression assume that the coefficient functions are smooth (usually they are assumed to belong to the Soblev space), and impose smoothness regularities in various ways. However, the smoothness assumption makes it difficult to model the associations between high local variations in response curve and predictor curves. We model the coefficient functions in a more general family of function spaces, where various levels of local variations are possible. We propose a new regularization method to replace the traditional smoothing method in functional data analysis, and apply it to our recently developed signal compression method in function-on-function regression. In addition to capturing the association between high local variations, such as rapid peaks, this method has good prediction performance and can handle multiple functional predictors with thousands of observation time points.