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Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework
Joint Authors
Luo, Xuan
Zhou, Fanyin
Ma, Yunbei
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-01-13
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We consider functional data analysis when the observations at each location are functional rather than scalar.
When the dynamic of underlying functional-valued process at each location is of interest, it is desirable to recover partial derivatives of a sample function, especially from sparse and noise-contaminated measures.
We propose a novel approach based on estimating derivatives of eigenfunctions of marginal kernels to obtain a representation for functional-valued process and its partial derivatives in a unified framework in which the number of locations and number of observations at each location for each individual can be any rate relative to the sample size.
We derive almost sure rates of convergence for the procedures and further establish consistency results for recovered partial derivatives.
American Psychological Association (APA)
Ma, Yunbei& Zhou, Fanyin& Luo, Xuan. 2020. Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1174547
Modern Language Association (MLA)
Ma, Yunbei…[et al.]. Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework. Journal of Applied Mathematics No. 2020 (2020), pp.1-17.
https://search.emarefa.net/detail/BIM-1174547
American Medical Association (AMA)
Ma, Yunbei& Zhou, Fanyin& Luo, Xuan. Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1174547
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174547