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Symmetry
Special Issues
Applications Based on Symmetry/Asymmetry in Functional Data Analysis
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Applications Based on Symmetry/Asymmetry in Functional Data Analysis

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 3692

Special Issue Editor

Prof. Nengxiang Ling

E-Mail Website
Guest Editor
School of Mathematics, Hefei University of Technology, Hefei, China
Interests: functional data analysis

Special Issue Information

Dear Colleague,

Progress in science and technology, both in the collection and storage of data, is now providing us with datasets such as curves and surfaces or images instead of scalars or multivariate vectors. These kinds of datasets display infinite dimensional or functional features and are usually called functional datasets, which occur in chemometrics, engineering, phonetics, etc. Statistical methodologies handling functional data are methods for functional data analysis (FDA), which was first proposed by Ramsay in 1991. Then, Ramsay and Silverman published the monograph "Functional Data Analysis" in 1997. The failure of standard multivariate analysis, numerous application fields and the new theoretical challenges motivate the statistical community to develop new methods in FDA.

In this Special Issue of the prestigious journal Symmetry, we will highlight notable advances in FDA, including theories, methods and techniques, in the fields of mathematical analysis and functional analysis, in which the concept of symmetry plays an essential role. The main objective of this Special Issue is to bring together original research in statistical machine learning and data mining from academia, industry, others in a relaxed and stimulating atmosphere to focus on the development of theories, methods and applications of statistical learning in functional data.

Topics include, but are not limited to, FDA, big data analysis, classification, computational biology, covariance estimation, graphical models, high-dimensional data, learning theory, model selection, network data analysis, signal and image processing, etc.

Prof. Nengxiang Ling
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

19 pages, 509 KiB  
Article
A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs
by Simeng Li, Dianliang Deng and Yuecai Han
Symmetry 2024, 16(4), 389; https://doi.org/10.3390/sym16040389 - 26 Mar 2024
Viewed by 1018
Abstract
In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential [...] Read more.
In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT). Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Functional Data Analysis)
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26 pages, 515 KiB  
Article
Combination Test for Mean Shift and Variance Change
by Min Gao, Xiaoping Shi, Xuejun Wang and Wenzhi Yang
Symmetry 2023, 15(11), 1975; https://doi.org/10.3390/sym15111975 - 25 Oct 2023
Cited by 1 | Viewed by 1836
Abstract
This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the [...] Read more.
This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Functional Data Analysis)
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