Partial Derivative Estimation for Underlying Functional‐Valued Process in a Unified Framework

Yunbei Ma, Fanyin Zhou and Xuan Luo

Journal of Applied Mathematics, 2020, vol. 2020, issue 1

Abstract: 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.

Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2020/6086983

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2020:y:2020:i:1:n:6086983

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().