A wavelet-based method in aggregated functional data analysis

TL;DR

This paper introduces a Bayesian wavelet shrinkage approach for estimating component curves in aggregated functional data, effectively capturing local features like discontinuities and spikes, and compares it with spline methods through simulations and real data application.

Contribution

It presents a novel wavelet-based Bayesian shrinkage method for component curve estimation in aggregated functional data analysis, emphasizing local feature detection.

Findings

The proposed method accurately estimates component functions with local features.

Simulation results show improved performance over spline-based methods.

Application to Tecator dataset demonstrates practical effectiveness.

Abstract

In this paper we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method and its results are compared with a spline-based method. An application on the so called tecator dataset is also provided.