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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24718 |
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| _version_ | 1866911545071501312 |
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| 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 |