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 method using the approximated Bayes factor, a score‐type test, and the estimating equations. The decision of rejecting (or not) the null hypothesis is made using the Frequentist p ‐values. We also studied the asymptotic properties of our method. We compare our detecting method to the alternative method regarding the type‐I error and power under various simulation settings. We demonstrate the advantages of our method by applying two real datasets: functional data of drug‐exposed glioblastoma cell line and diffusion tensor imaging tractography.