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.

翻译：本文研究了在严格正的随机误差服从Gamma分布、且误差通过AR(1)和ARFIMA过程形成相关结构的模型中，从聚合曲线观测值估计组成曲线（即聚合函数数据）的统计问题。该问题出现在多个知识领域，例如化学计量学中，需要根据比尔-朗伯定律从物质各组分吸收曲线的聚合曲线中估计其吸收曲线。在此背景下，我们提出基于贝叶斯小波的方法，在函数型数据分析框架内估计组成函数。由于小波基对函数的表示特性，该方法能够准确估计具有重要局部特征（如间断点、峰值和振荡）的曲线。我们通过计算模拟以及实际数据应用进一步评估了所提方法的性能。