A Changepoint Detection Method for Profile Variance

TL;DR

This paper introduces a wavelet-based changepoint detection method that accurately monitors noise variability in functional profiles, accommodating diverse functions and profile variations, with demonstrated efficiency through extensive simulations.

Contribution

It presents a novel wavelet-based approach for detecting changes in noise variance in functional profiles, capable of handling complex and contaminated data structures.

Findings

Effective detection of variance changes demonstrated in simulations

Method robust to profile functional contamination

Outperforms existing techniques in accuracy and efficiency

Abstract

A wavelet-based changepoint method is proposed that determines when the variability of the noise in a sequence of functional profiles goes out-of-control from a known, fixed value. The functional portion of the profiles are allowed to come from a large class of functions and may vary from profile to profile. The proposed method makes use of the orthogonal properties of wavelet projections to accurately and efficiently monitor the level of noise from one profile to the next. Several alternative implementations of the estimator are compared on a variety of conditions, including allowing the wavelet noise subspace to be substantially contaminated by the profile's functional structure. The proposed method is shown to be very efficient at detecting when the variability has changed through an extensive simulation study.