Effective dimension reduction for sparse functional data

We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the...

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Bibliographic Details
Published inBiometrika Vol. 102; no. 2; p. 421
Main Authors Yao, F, Lei, E, Wu, Y
Format Journal Article
LanguageEnglish
Published England 01.06.2015
Subjects
Effective dimension reduction
Sparse functional data
Cumulative slicing
Inverse regression
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Summary:We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and decaying structures of the predictor process and the effective dimension reduction space. A simulation study and an application illustrate the superior finite-sample performance of the method.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asv006