Liu, H. orcid.org/0000-0002-3442-1722 and Houwing-Duistermaat, J. (2023) On estimation of covariance function for functional data with detection limits. Journal of Nonparametric Statistics. ISSN 1048-5252
Abstract
In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches ignore the problem by just filling in the value of the detection limit for the missing observations for the estimation of the mean and covariance function, which yield inaccurate estimation. Inspired by our recent work [Liu and Houwing-Duistermaat (2022), ‘Fast Estimators for the Mean Function for Functional Data with Detection Limits’, Stat, e467.] in which novel estimators for mean function for data subject to detection limit are proposed, in this paper, we will propose a novel estimator for the covariance function for sparse and dense data subject to a detection limit. We will derive the asymptotic properties of the estimator. We will compare our method to the standard method, which ignores the detection limit, via simulations. We will illustrate the new approach by analysing biomarker data subject to a detection limit. In contrast to the standard method, our method appeared to provide more accurate estimates of the covariance. Moreover its computation time is small.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. |
Keywords: | Functional data analysis; informative missing; detection limit; local constant covariance estimation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Nov 2023 14:27 |
Last Modified: | 20 Nov 2023 14:27 |
Status: | Published online |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/10485252.2023.2258999 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:205508 |
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