Panel data segmentation under finite time horizon

TL;DR

This paper investigates nonparametric change point estimation in panel data with a fixed sample size, proposing covariance-based weighting schemes for consistency and providing bounds on change-to-noise ratios, supported by simulations.

Contribution

It introduces a covariance-based extension of weighting schemes for change point detection in panel data with finite samples, ensuring consistency under dependence.

Findings

Proposed a consistent covariance-based weighting scheme.

Derived bounds on change-to-noise ratio for consistency.

Validated methods through simulation studies.

Abstract

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even provide consistency in the i.i.d. setting when the noise is too dominant. Hence, on the one hand, we propose a consistent covariance-based extension of existing weighting schemes and discuss straightforward estimates of those weighting schemes. The performance will be demonstrated empirically in a simulation study. On the other hand, we derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.