Analysis of Functional Data without Dimension Reduction: Tests for Covariance Operators and Changepoint Problems
Final Report Abstract
Functional data arises in many applications and the main strategy for statistical inference is dimension reduction: The data is projected on a finite-dimensional space with techniques such as functional principal components. The aim of this project was to develop fully functional methods without dimension reduction for change-point detection in more complicated data situations: We have investigated test for hypothesis not only on the functional mean, but on the covariance operator, treating cross covariance operators and autocovariance operators under a unified framework. We have developed a robust test for shifts in location based on spatial signs and also propose estimators for the time and location of the change. The asymptotic distribution of our test statistics depends on infinite-dimensional nuisance parameters and thus cannot be used for obtaining critical values easily. For this reason, we use various bootstrap methods. We have improved the choice of the block length for the non-overlapping block bootstrap. For nondegenerate Hilbert-spacevalued U-statistic, a new variant of the dependent wild bootstrap has been developed. We are working on extending the functional autoregressive sieve bootstrap to partial sums, so that we can apply it to change-point tests.
Publications
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Bootstrapping covariance operators of functional time series. Journal of Nonparametric Statistics, 32(3), 648-666.
Sharipov, Olimjon Sh. & Wendler, Martin
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Block Length Choice for the Bootstrap of Dependent Panel Data–a Comment on Choi and Shin
L. Wegner, M. Wendler
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Change-point detection based on weighted two-sample U-statistics. Electronic Journal of Statistics, 16(1).
Dehling, Herold; Vuk, Kata & Wendler, Martin
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Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap. Statistical Papers (2024, 6, 5).
Wegner, Lea & Wendler, Martin
