Abstract

In this paper, we study the estimation and inference of change points

under a functional linear regression model with changes in the slope function.

We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is computationally efficient as well as achieving consistency in mul-

tiple change point detection.

This algorithm utilizes the predictive power of

piece-wise constant functional linear regression models in the reproducing kernel

Hilbert space framework. We further propose a refinement step that improves the

localization rate of the initial estimator output by FRBS, and derive asymptotic

distributions of the refined estimators for two different regimes determined by

the magnitude of a change. To facilitate the construction of confidence intervals

for underlying change points based on the limiting distribution, we propose a

consistent block-type long-run variance estimator. Our theoretical investigation

accommodates temporal dependence and heavy-tails in both the functional covariates and the measurement errors. Empirical performance of our method is

demonstrated through extensive simulation studies and applications to financial

and economic datasets.

Information

Preprint No.SS-2024-0234
Manuscript IDSS-2024-0234
Complete AuthorsShivam Kumar, Haotian Xu, Haeran Cho, Daren Wang
Corresponding AuthorsHaotian Xu
Emailshaotian.xu2@icloud.com

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Supplementary Materials

We collect extensive simulation studies, additional real data analysis and

all the technical details in the online supplementary material.

Supplementary materials are available for download.