Wavelet estimation in aggregated functional data analysis

• Grant number: 24/11042-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2024
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Alex Rodrigo dos Santos Sousa
• Grantee: João Victor Siqueira Rodrigues
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project, we address the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as aggregated functional data, within an additive model with Gaussian errors. This problem arises in various fields of knowledge, such as chemometrics, when absorbance curves of constituents of a given substance need to be estimated from its aggregated absorbance curve, according to the Beer-Lambert Law. We propose to study the use of wavelet bases for representing the constituent curves to be estimated. This approach has the advantage of estimating curves with important local characteristics, such as discontinuities, peaks, and oscillations, due to the properties of wavelet basis expansion of functions. We propose the theoretical study of the estimators, the evaluation of the performance of the proposed method through computational simulations and applications to real data.