A nonlinear mixed effects approach to the registration of functional data

• Ano de defesa: 2024
• Autor(a) principal: Ferreira, Felipe Toledo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Alinhamento de curvas; Análise de dados funcionais; Curve registration; Functional data analysis; Inferência não paramétrica; Modelos mistos não lineares; Nonlinear mixed models; Nonparametric statistics; Ondaletas; P-splines; Smoothing; Suavização; Wavelets
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-04112024-163842/

A chief concern for most methods of standard multivariate data analysis is performing inference concerning data of finite, albeit possibly very high, dimensions; in contrast to this lies the field of functional data analysis (FDA), dealing with data that is intrinsically infinite dimensional (e.g., curves, surfaces, etc.), introducing novel complications to the inferential process. We highlight two significant components of FDA: curve \"smoothing\" and \"registration\"; the former is widely studied in nonparametric statistics, whilst the latter has a narrower background, referring to the adjustment of misaligned observed curves. Curve registration is often performed as a form of data preprocessing, prior to smoothing, though Rakêt et al., 2014 found that this preprocessing approach results in worse model estimates when compared to tools for simultaneous smoothing and registration, and suggested an approach based on nonlinear mixed effects models which performs smoothing and registration simultaneously. This development follows other model-based implementations, such as Telesca and Inoue, 2008, based upon Bayesian hierarchical modelling, Fu and Heckman, 2019, based on the stochastic approximation EM algorithm, and Claeskens et al., 2021, similarly based on nonlinear mixed effects models; these mainly focus on the usage of B-splines for smoothing the observed functions. We propose and implement an adaptation of these models via a wavelet basis expansion approach, as it provides a more flexible tool for curves with rougher and more localized features (Morris and Carroll, 2006), as opposed to smoother global trends that behave well under B-splines. We provide a comparative study of the performance of the herein cited methods through simulations, as well as real data applications, contrasting the B-spline and wavelet implementations.