Vitor Ribas Perrone | Searcharxiv

arXiv2026

FunctionalCalibration: an R package for estimation in aggregated functional data model

Aggregated functional data arise in a variety of applications where only linear combinations of latent functional components are observed. A prominent example is found in chemometrics through the Beer-Lambert law. This paper introduces the FunctionalCalibration package for R, which provides tools for estimating constituent curves from aggregated functional observations under additive error models. The package implements calibration methods based on B-spline and wavelet basis expansions, allowing the recovery of smooth as well as locally irregular component functions. In addition, it includes simulation tools, visualization functions, and procedures for estimating weights in prediction problems. The package is illustrated through simulated and real datasets, demonstrating its flexibility and practical applicability in functional calibration problems.

stat.CO↗

arXiv2026

Wavelet-based estimation in aggregated functional data with positive and correlated errors

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.

stat.ME↗