Enhanced Change-Point Detection in Functional Means

TL;DR

This paper introduces a novel dimension reduction method for change-point detection in functional data, significantly improving detection power especially in noisy or complex scenarios.

Contribution

It develops an efficient basis function selection technique that enhances change detection in functional means, outperforming existing methods.

Findings

Proposed method detects small or shrinking changes asymptotically almost surely.

Numerical simulations show superior performance over functional principal component methods.

Application to humidity data demonstrates practical effectiveness.

Abstract

A new dimension reduction methodology for change-point detection in functional means is developed in this paper. The major advantage and novelty of the proposed method is its efficiency in selecting basis functions that capture the change, or jump, of functional means, leading to higher detection power, especially when the functions cannot be sufficiently explained by a small number of basis functions or are contaminated by random noises. The throughly developed theoretical results demonstrate that, even when the change shrinks to zero, the proposed approach can still detect the change asymptotically almost surely. The numerical simulation studies justify the superiority of the proposed approach to the method based on functional principal components and the fully functional approach without dimension reduction. An application to annual humidity trajectories was also included to illustrate the practical superiority of the developed approach.