Saved in:
Bibliographic Details
Main Authors: Sousa, Alex Rodrigo dos Santos, Rodrigues, João Victor Siqueira, Perrone, Vitor Ribas, Rocha, Raul Gomes
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.24718
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911545071501312
author Sousa, Alex Rodrigo dos Santos
Rodrigues, João Victor Siqueira
Perrone, Vitor Ribas
Rocha, Raul Gomes
author_facet Sousa, Alex Rodrigo dos Santos
Rodrigues, João Victor Siqueira
Perrone, Vitor Ribas
Rocha, Raul Gomes
contents We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as \textit{aggregated functional data}, in models with strictly positive random errors following a Gamma distribution and correlated errors structured through AR(1) and ARFIMA processes. This problem arises in several areas of knowledge, such as chemometrics, for example, when absorbance curves of the constituents of a given substance must be estimated from its aggregated absorbance curve according to the Beer--Lambert law. In this context, we propose Bayesian wavelet-based methods to estimate the component functions within a functional data analysis framework. This approach has the advantage of accurately estimating curves with important local features, such as discontinuities, peaks, and oscillations, due to the representation properties of functions in wavelet bases. We further evaluate the performance of the proposed method through computational simulations, as well as applications to real data.
format Preprint
id arxiv_https___arxiv_org_abs_2603_24718
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Wavelet-based estimation in aggregated functional data with positive and correlated errors
Sousa, Alex Rodrigo dos Santos
Rodrigues, João Victor Siqueira
Perrone, Vitor Ribas
Rocha, Raul Gomes
Methodology
We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as \textit{aggregated functional data}, in models with strictly positive random errors following a Gamma distribution and correlated errors structured through AR(1) and ARFIMA processes. This problem arises in several areas of knowledge, such as chemometrics, for example, when absorbance curves of the constituents of a given substance must be estimated from its aggregated absorbance curve according to the Beer--Lambert law. In this context, we propose Bayesian wavelet-based methods to estimate the component functions within a functional data analysis framework. This approach has the advantage of accurately estimating curves with important local features, such as discontinuities, peaks, and oscillations, due to the representation properties of functions in wavelet bases. We further evaluate the performance of the proposed method through computational simulations, as well as applications to real data.
title Wavelet-based estimation in aggregated functional data with positive and correlated errors
topic Methodology
url https://arxiv.org/abs/2603.24718