Registration and estimation for functional generalized linear model

Functional data analysis has recently concentrated on the challenges of registration and estimation. Our research team has developed an innovative model that enables the simultaneous registration and estimation of multivariate functional data. This approach eliminates the need for pre-smoothing, thereby improving computational efficiency. We utilize the inverse warping function in conjunction with generalized functional principal component analysis (GFPCA) to approximate the covariance structure effectively. The inverse warping function, population mean function, and orthonormal eigenfunctions are estimated using B-spline methods. We have derived the joint probability distribution and established its asymptotic normality. Through extensive simulation studies and real data analyses, we compare our method with existing approaches and demonstrate its exceptional performance, showcasing superior fitting capabilities.