Advances in Functional and Topological Data Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (27 December 2024) | Viewed by 2779

Special Issue Editors


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Guest Editor
Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, 83200 Samos, Greece
Interests: functional analysis (partially ordered linear spaces); convex analysis; vector optimization; financial mathematics (mathematical aspects of risk measurement and rsk management; derivatives’ pricing); mathematical economics (general equilibrium theory)
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Guest Editor
Department of Accounting and Finance, Hellenic Mediterranean University, Heraklion, Greece
Interests: computational statistics; digital finance; extreme value theory; financial econometrics; quantitative finance; risk management; volatility and times series analysis
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Accounting and Finance, Hellenic Mediterranean University, Heraklion, Crete, Greece
Interests: financial economics; financial econometrics; risk management; banking
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit papers to this Special Issue, "Advances in Functional and Topological Data Analysis".

The aim of this Special Issue is to advance mathematical Data Analysis in relation to Functional Analysis and Topology. This approach supports Econometrics and Finance research. Potential papers may use Topology and Functional Analysis to fit regression models or multivariate analysis and test metrics in a clear way. This Special Issue also welcomes papers on realized Data Analysis to encourage the use of a variety of models that rely on Functional Analysis and Topology. The scope is to support interaction between applied mathematicians and economists.

Suggested themes/keywords:   

  • Applications of operator theory in statistics;
  • Applications of topology in statistics; 
  • Goodness-of-fit metrics for regression models;
  • Goodness-of-fit metrics for parameters' estimation; 
  • Space data analysis;
  • Significance of variables in regression and multivariate analysis;
  • Model uncertainty;
  • Components of uncertainty and their modeling;
  • Metric spaces and manifolds in statistics and econometrics.

In this Special Issue, reviews are also welcome.

We look forward to receiving your contributions.

Dr. Christos Kountzakis
Dr. Konstantinos Gkillas
Prof. Dr. Christos Floros
Guest Editors

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. Axioms 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.

Keywords

  • Functional data analysis
  • Topological data analysis
  • Model uncertainty
  • Applications of operator theory in statistics
  • Applications of topology in statistics
  • Goodness-of-fit metrics for regression models
  • Goodness-of-fit metrics for parameters' estimation
  • Space data analysis
  • Metric spaces and manifolds in statistics and econometrics

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Published Papers (3 papers)

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Research

21 pages, 403 KiB  
Article
Spatio-Functional Nadaraya–Watson Estimator of the Expectile Shortfall Regression
by Mohammed B. Alamari, Fatimah A. Almulhim, Zoulikha Kaid and Ali Laksaci
Axioms 2024, 13(10), 678; https://doi.org/10.3390/axioms13100678 - 30 Sep 2024
Viewed by 614
Abstract
The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of [...] Read more.
The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of expected shortfall regression with an expectile risk model. A spatio-functional Nadaraya–Watson estimator of the studied metric risk is constructed. The main asymptotic results of this work are the establishment of almost complete convergence under a mixed spatial structure. The claimed asymptotic result is obtained under standard assumptions covering the double functionality of the model as well as the data. The impact of the spatial interaction of the data in the proposed risk metric is evaluated using simulated data. A real experiment was conducted to measure the feasibility of the Spatio-Functional Expectile Shortfall Regression (SFESR) in practice. Full article
(This article belongs to the Special Issue Advances in Functional and Topological Data Analysis)
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20 pages, 1968 KiB  
Article
Generalized Partially Functional Linear Model with Interaction between Functional Predictors
by Weiwei Xiao, Kejing Mao and Haiyan Liu
Axioms 2024, 13(9), 583; https://doi.org/10.3390/axioms13090583 - 27 Aug 2024
Viewed by 696
Abstract
This paper proposes a generalized partially functional linear model with interaction terms. It is suitable for cases where the response variable is scalar, and the predictor variables include a mix of functional and scalar types, while considering the correlations among functional predictor variables. [...] Read more.
This paper proposes a generalized partially functional linear model with interaction terms. It is suitable for cases where the response variable is scalar, and the predictor variables include a mix of functional and scalar types, while considering the correlations among functional predictor variables. The model uses principal component analysis for dimensionality reduction, employs maximum likelihood estimation to obtain parameter values, proves the asymptotic properties of the estimates, and validates the model’s accuracy through data simulation experiments. Finally, the proposed model was applied to investigate the influence of air quality, climate factors, and medical and social indicators, along with their interactions, on cancer incidence, which is a binary response. Full article
(This article belongs to the Special Issue Advances in Functional and Topological Data Analysis)
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11 pages, 264 KiB  
Article
On Modulus Statistical Convergence in Partial Metric Spaces
by Francisco Javier García-Pacheco and Ramazan Kama
Axioms 2024, 13(6), 388; https://doi.org/10.3390/axioms13060388 - 8 Jun 2024
Viewed by 949
Abstract
Modulus statistical convergence has been studied in very different general settings such as topological spaces and uniform spaces. In this manuscript, modulus statistical convergence is defined and studied in partial metric spaces. Full article
(This article belongs to the Special Issue Advances in Functional and Topological Data Analysis)
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