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Wavelet Funcional Data Analysis: Foundations and Applications

Grant number: 16/24469-6
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2017
Effective date (End): February 25, 2021
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Statistics
Principal Investigator:Aluísio de Souza Pinheiro
Grantee:Rodney Vasconcelos Fonseca
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:13/00506-1 - Time series, wavelets and functional data analysis, AP.TEM
Associated scholarship(s):18/06874-6 - Statistical analysis of temporal graph wavelets statistical analysis of temporal graph wavelets, BE.EP.DR


Functional data analysis has gained a lot of attention in the past few years. One very promising methodological paradigm is given by wavelet analysis. This methods have some general properties which are particularly interesting for FDA: parsimony, asymptotics, and computational performance.Wavelets are ideally suited for the formulation of computationally and statistically efficient methodologies on Functional data Analysis. We refer to Donoho and Johnstone (1998); Abramovich et al. (2004); Fan and Koo (2002); Klemelä (2006); and Morettin, Pinheiro and Vidakovi (2016) for details.Applications of statistical models for functional data is large and continuously growing. There are several major open questions which we hope to answer theoretically, such as:(i) Asymptotic properties of wavelet estimators, and its relative performance against other paradigms.(ii) Parsimonious wavelet representation.(iii) Optimal wavelet-based tests.(iv) Aletrnative underlying generating stochastic process to the ubiquotous Brownian motion.We will develop theoretical models based on Stochastic Differential Equations which generalize the current models in two main aspects:(A) Generating stochastic process, specially by CTARMA processes and Fractional Brownian motions.(B) Stochastic volatility and/or non-stationary models.Three main areas of application we will pursue are:(i) High frequency financial data and volatility models.(ii) Multidimensional models and high resolution satellite time series.(iii) Genomincs and proteinomics.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FONSECA, RODNEY V.; PINHEIRO, ALUISIO. Wavelet estimation of the dimensionality of curve time series. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, v. 72, n. 5, p. 1175-1204, . (16/24469-6, 13/00506-1, 18/04654-9)
FONSECA, RODNEY V.; NEGRI, ROGERIO G.; PINHEIRO, ALUISIO; ATTO, ABDOURRAHMANE MAHAMANE. Wavelet Spatio-Temporal Change Detection on Multitemporal SAR Images. IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, v. 16, p. 11-pg., . (21/04513-9, 18/04654-9, 16/24469-6, 21/01305-6)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
FONSECA, Rodney Vasconcelos. Some wavelet-based contributions to functional data analysis. 2021. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.

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