Some wavelet-based contributions to functional data analysis

Author(s)

Rodney Vasconcelos Fonseca

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2021-03-10

Examining board members

Aluísio de Souza Pinheiro; Luiz Koodi Hotta; Ronaldo Dias; Chang Chiann; Pedro Alberto Morettin

• Advisor: Aluísio de Souza Pinheiro

Abstract

Functional data analysis is a field widely disseminated in data analysis literature. The popularity of this kind of data is due to high measurement and storage capacity of modern equipments. Besides such large availability of functional data, the methodology that treats curves as observations also brings challenges to common methods in statistical analysis, such as high dimensionality, local features, regularity control, dependence and irregularity of some functional domains, for example. Wavelet methods are well suited to deal with such problems, having as main characteristics its asymptotic optimality, numerical feasibility and parsimonious representations. The goal of this work is to present how wavelet representations can be used in the context of functional data to estimate the dimensionality of curve time series and to show how the wavelet transform can be adapted for the case where functions are observed in the nodes of a graph. Additionally, we present results involving U and V-statistics for mixing processes and discuss how this problem can be considered to analyze random variables associated to a graph. Applications of the discussed techniques are performed on real data about fertility rates, satellite images and taxi trips, illustrating how the discussed methods can be employed and interpreted (AU)

• FAPESP's process: 16/24469-6 - Wavelet Funcional Data Analysis: Foundations and Applications
• Grantee: Rodney Vasconcelos Fonseca
• Support Opportunities: Scholarships in Brazil - Doctorate