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Mathematics
Special Issues
Contemporary Contributions to Statistical Modelling and Data Science
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Contemporary Contributions to Statistical Modelling and Data Science

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 5912

Special Issue Editors

Dr. Sollie Millard

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Guest Editor
Department of Statistics, University of Pretoria, Pretoria, South Africa
Interests: data science; analytics; statistics; mixture modelling
Dr. Frans Kanfer

E-Mail Website
Guest Editor
Department of Statistics, University of Pretoria, Pretoria, South Africa
Interests: data science; analytics; statistics; mixture modelling; sequential analysis
Prof. Dr. Samuel Manda

E-Mail Website
Guest Editor
Department of Statistics, University of Pretoria, Pretoria, South Africa
Interests: Bayesian multivariate spatial statistics methods; complex sample survey analysis methods; Bayesian nonparametric methods for correlated survival statistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, there has been significant growth in various aspects of statistical modelling in both theoretical and applied contexts. This includes developments in model-based clustering, mixture modelling, mixture regression, computational analytics, circular data analytics, multilevel models, differential networks, penalty-based feature section, non- and semi-parametric extensions, and many more. The aim of this Mathematics Special Issue considers recent and modern contributions in the general realm of statistical modelling and data science. We welcome methodological, computational, as well as applied papers making a substantial contribution to the body of statistical and data science literature. Specific emphasis will be placed on non- and semi-parametric contributions. Papers can be submitted to “Mathematics” by selecting the Special Issue “Contemporary Contributions to Statistical Modelling and Data Science”. Note that all submitted papers should be within the general scope of the Mathematics journal.

Dr. Sollie Millard
Dr. Frans Kanfer
Prof. Dr. Samuel Manda
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • mixture modelling
  • mixture regression
  • circular statistics
  • non-parametric modelling
  • semi-parametric modelling
  • classification
  • penalty based feature selection

Published Papers (5 papers)

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Research

9 pages, 300 KiB  
Article
Multicollinearity and Linear Predictor Link Function Problems in Regression Modelling of Longitudinal Data
by Mozhgan Taavoni, Mohammad Arashi and Samuel Manda
Mathematics 2023, 11(3), 530; https://doi.org/10.3390/math11030530 - 18 Jan 2023
Cited by 1 | Viewed by 1134
Abstract
In the longitudinal data analysis we integrate flexible linear predictor link function and high-correlated predictor variables. Our approach uses B-splines for non-parametric part in the linear predictor component. A generalized estimation equation is used to estimate the parameters of the proposed model. We [...] Read more.
In the longitudinal data analysis we integrate flexible linear predictor link function and high-correlated predictor variables. Our approach uses B-splines for non-parametric part in the linear predictor component. A generalized estimation equation is used to estimate the parameters of the proposed model. We assess the performance of our proposed model using simulations and an application to an analysis of acquired immunodeficiency syndrome data set. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
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16 pages, 307 KiB  
Article
Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models
by Bo Jiang and Yongge Tian
Mathematics 2023, 11(1), 182; https://doi.org/10.3390/math11010182 - 29 Dec 2022
Viewed by 820
Abstract
This paper provides a complete matrix analysis on equivalence problems of estimation and inference results under a true multivariate linear model Y=XΘ+Ψ and its misspecified form Y=XΘ+ZΓ+Ψ with an augmentation [...] Read more.
This paper provides a complete matrix analysis on equivalence problems of estimation and inference results under a true multivariate linear model Y=XΘ+Ψ and its misspecified form Y=XΘ+ZΓ+Ψ with an augmentation part ZΓ through the cogent use of various algebraic formulas and facts in matrix analysis. The coverage of this study includes the matrix derivations of the best linear unbiased estimators under the true and misspecified models, and the establishment of necessary and sufficient conditions for the different estimators to be equivalent under the model assumptions. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
19 pages, 2905 KiB  
Article
High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market
by Azam Kheyri, Andriette Bekker and Mohammad Arashi
Mathematics 2022, 10(22), 4232; https://doi.org/10.3390/math10224232 - 12 Nov 2022
Viewed by 1223
Abstract
This article studies the estimation of the precision matrix of a high-dimensional Gaussian network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize a penalized likelihood function where the elastic net-type penalty is considered as a combination of a [...] Read more.
This article studies the estimation of the precision matrix of a high-dimensional Gaussian network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize a penalized likelihood function where the elastic net-type penalty is considered as a combination of a norm-one penalty and a targeted Frobenius norm penalty. Numerical illustrations demonstrate that our proposed methodology is a competitive candidate for high-dimensional precision matrix estimation compared to some existing alternatives. We demonstrate the relevance and efficiency of GSOS using a foreign exchange markets dataset and estimate dependency networks for 32 different currencies from 2018 to 2021. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
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21 pages, 3023 KiB  
Article
An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts
by Ané van der Merwe and Johannes T. Ferreira
Mathematics 2022, 10(21), 4141; https://doi.org/10.3390/math10214141 - 06 Nov 2022
Viewed by 987
Abstract
Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the [...] Read more.
Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the error terms. In order to address the equidispersion restriction of the Poisson distribution, various alternative considerations have been investigated in such an integer environment. This paper, inspired by the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a compound Poisson Lindley model for the error terms. The systematic construction of this model is offered and motivated, and is analysed comparatively against common alternate candidates with a number of simulation and data analyses. This work provides insight into noncentral-type behaviour in both the continuous Lindley model and in the discrete case for meaningful application and consideration in integer autoregressive environments. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
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13 pages, 596 KiB  
Article
Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method
by Rasoul Lotfi, Davood Shahsavani and Mohammad Arashi
Mathematics 2022, 10(21), 4069; https://doi.org/10.3390/math10214069 - 01 Nov 2022
Cited by 1 | Viewed by 1161
Abstract
Classification using linear discriminant analysis (LDA) is challenging when the number of variables is large relative to the number of observations. Algorithms such as LDA require the computation of the feature vector’s precision matrices. In a high-dimension setting, due to the singularity of [...] Read more.
Classification using linear discriminant analysis (LDA) is challenging when the number of variables is large relative to the number of observations. Algorithms such as LDA require the computation of the feature vector’s precision matrices. In a high-dimension setting, due to the singularity of the covariance matrix, it is not possible to estimate the maximum likelihood estimator of the precision matrix. In this paper, we employ the Stein-type shrinkage estimation of Ledoit and Wolf for high-dimensional data classification. The proposed approach’s efficiency is numerically compared to existing methods, including LDA, cross-validation, gLasso, and SVM. We use the misclassification error criterion for comparison. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
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