Sequential block bootstrap in a Hilbert space with application to change point analysis

TL;DR

This paper introduces a novel bootstrap-based test for detecting structural changes in functional data within a Hilbert space framework, supported by a new functional central limit theorem and applied to hydrological data.

Contribution

It develops a new block bootstrap method in a Hilbert space setting and establishes a corresponding functional central limit theorem, enabling change point detection in complex data.

Findings

Effective detection of change points in functional data.

Bootstrap method provides reliable critical values.

Application to hydrological data demonstrates practical utility.

Abstract

A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a Hilbert space is required. The test can also be used to detect changes in the marginal distribution of random vectors, which is supplemented by a simulation study. Our methods are applied to hydrological data from Germany.