Detection of Unknown Functional Departure in Generalized Functional Regression

ABSTRACT Detecting statistical differences among functional dataset or streaming signal dataset is of interest to many diverse fields, including neurophysiology, imaging, biomedical engineering, and public health. For example in our study, our interest is to provide the guideline for detecting the lowest drug dosage level for glioblastoma as quickly as possible in which the intensity functional curves are different among dosage groups. However, such functional data often have unknown and nonlinear massive correlated curves that lead to difficulties in detecting their significant differences without explicit likelihood functions. Existing detecting procedures mainly test a linear, quadratic, or specific parametric form of departure and require explicit likelihood functions due to estimating specific models. In this paper, we propose a flexible detecting method to test any unknown functional departure in a generalized functional regression without estimating models. We develop our detecting method under a generalized semiparametric functional model framework in which the explicit likelihood function does not exist. We develop our detecting metho