Trimmed Mean for Partially Observed Functional Data

TL;DR

This paper introduces a trimmed mean estimator for partially observable functional data, demonstrating its theoretical consistency and superior robustness over the ordinary mean through simulation studies.

Contribution

It extends the trimmed mean concept to partially observable functional data and proves its strong consistency, addressing a gap in existing statistical methods.

Findings

The proposed estimator is more accurate than the ordinary mean.

The estimator is robust to partial observability.

Simulation results confirm the theoretical advantages.

Abstract

In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data integration depth for partially observable functions, as proposed by Elias et al. (2023), and the trimmed-mean estimator method along with its consistency proof introduced by Fraiman and Muniz (2001) for completely observable functions. We introduce the concept of trimmed mean specifically for partially observable functional data. Additionally, we address several theoretical and practical issues, including a proof of the strong consistency of the proposed trimmed mean, and we provide a simulation study. The results demonstrate that our estimator outperforms the ordinary mean in terms of accuracy and robustness when applied to partially observable functional data.