Segmentation of the mean of heteroscedastic data via cross-validation

TL;DR

This paper introduces a new change-point detection method using cross-validation that effectively identifies shifts in the mean of heteroscedastic signals, outperforming traditional methods that lack robustness to noise variability.

Contribution

It proposes a novel family of change-point detection procedures based on cross-validation, specifically designed to handle heteroscedastic data where noise variance is unknown.

Findings

Cross-validation methods are effective in heteroscedastic settings.

Proposed procedures outperform existing methods in robustness.

Application to CGH data demonstrates practical utility.

Abstract

This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. A new family of change-point detection procedures is proposed, showing that cross-validation methods can be successful in the heteroscedastic framework, whereas most existing procedures are not robust to heteroscedasticity. The robustness to heteroscedasticity of the proposed procedures is supported by an extensive simulation study, together with recent theoretical results. An application to Comparative Genomic Hybridization (CGH) data is provided, showing that robustness to heteroscedasticity can indeed be required for their analysis.