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Mathematics
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Application of Regression Models, Analysis and Bayesian Statistics
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Application of Regression Models, Analysis and Bayesian Statistics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 6647

Special Issue Editors

Dr. Fernando Ferraz do Nascimento

E-Mail Website
Guest Editor
Department of Statistics, Federal University of Piaui, Teresina, Brazil
Interests: applied mathematics and statistics; Bayesian inference; regression models; extreme value theory; non-parametric models; stochastic models; time-series model; environmental data; financial data
Dr. Marcelo Bourguignon

E-Mail Website
Guest Editor
Department of Statistics, Federal University of Rio Grande do Norte, Natal 59078-970, RN, Brazil
Interests: statistical analysis; data analysis; statistics; statistical modeling; probability; simulation; applied statistics; econometric analysis; applied mathematics; modeling and simulation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Regression models and Bayesian analysis are two of the most important areas in the field of probability and statistics. The generality of the topic implies data analysis in practically all areas of knowledge. This Special Issue focuses on new approaches to regression models, using the Bayesian paradigm, applied in the most diverse areas of knowledge. Possible topics could include the following:

  1. Extreme value models;
  2. Spatial models;
  3. Quantile regression;
  4. Dynamic models;
  5. Environmental and climate change analysis;
  6. Econometrical data;
  7. Multivariate analysis.

Topics not listed above but related to the title are also welcome for submission.

Dr. Fernando Ferraz do Nascimento
Dr. Marcelo Bourguignon
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

  • regression models
  • Bayesian analysis
  • MCMC
  • environmental data
  • spatial models
  • financial data
  • extreme value theory

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Published Papers (4 papers)

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Research

20 pages, 1435 KiB  
Article
Modified Kibria–Lukman Estimator for the Conway–Maxwell–Poisson Regression Model: Simulation and Application
by Nasser A. Alreshidi, Masad A. Alrasheedi, Adewale F. Lukman, Hleil Alrweili and Rasha A. Farghali
Mathematics 2025, 13(5), 794; https://doi.org/10.3390/math13050794 - 27 Feb 2025
Viewed by 454
Abstract
This study presents a novel estimator that combines the Kibria–Lukman and ridge estimators to address the challenges of multicollinearity in Conway–Maxwell–Poisson (COMP) regression models. The Conventional COMP Maximum Likelihood Estimator (CMLE) is notably susceptible to the adverse effects of multicollinearity, underscoring the necessity [...] Read more.
This study presents a novel estimator that combines the Kibria–Lukman and ridge estimators to address the challenges of multicollinearity in Conway–Maxwell–Poisson (COMP) regression models. The Conventional COMP Maximum Likelihood Estimator (CMLE) is notably susceptible to the adverse effects of multicollinearity, underscoring the necessity for alternative estimation strategies. We comprehensively compare the proposed COMP Modified Kibria–Lukman estimator (CMKLE) against existing methodologies to mitigate multicollinearity effects. Through rigorous Monte Carlo simulations and real-world applications, our results demonstrate that the CMKLE exhibits superior resilience to multicollinearity while consistently achieving lower mean squared error (MSE) values. Additionally, our findings underscore the critical role of larger sample sizes in enhancing estimator performance, particularly in the presence of high multicollinearity and over-dispersion. Importantly, the CMKLE outperforms traditional estimators, including the CMLE, in predictive accuracy, reinforcing the imperative for judicious selection of estimation techniques in statistical modeling. Full article
(This article belongs to the Special Issue Application of Regression Models, Analysis and Bayesian Statistics)
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18 pages, 1047 KiB  
Article
Modified Liu Parameters for Scaling Options of the Multiple Regression Model with Multicollinearity Problem
by Autcha Araveeporn
Mathematics 2024, 12(19), 3139; https://doi.org/10.3390/math12193139 - 7 Oct 2024
Cited by 1 | Viewed by 1427
Abstract
The multiple regression model statistical technique is employed to analyze the relationship between the dependent variable and several independent variables. The multicollinearity problem is one of the issues affecting the multiple regression model, occurring in regard to the relationship among independent variables. The [...] Read more.
The multiple regression model statistical technique is employed to analyze the relationship between the dependent variable and several independent variables. The multicollinearity problem is one of the issues affecting the multiple regression model, occurring in regard to the relationship among independent variables. The ordinal least square is the standard method to evaluate parameters in the regression model, but the multicollinearity problem affects the unstable estimator. Liu regression is proposed to approximate the Liu estimators based on the Liu parameter, to overcome multicollinearity. In this paper, we propose a modified Liu parameter to estimate the biasing parameter in scaling options, comparing the ordinal least square estimator with two modified Liu parameters and six standard Liu parameters. The performance of the modified Liu parameter is considered, generating independent variables from the multivariate normal distribution in the Toeplitz correlation pattern as the multicollinearity data, where the dependent variable is obtained from the independent variable multiplied by a coefficient of regression and the error from the normal distribution. The mean absolute percentage error is computed as an evaluation criterion of the estimation. For application, a real Hepatitis C patients dataset was used, in order to investigate the benefit of the modified Liu parameter. Through simulation and real dataset analysis, the results indicate that the modified Liu parameter outperformed the other Liu parameters and the ordinal least square estimator. It can be recommended to the user for estimating parameters via the modified Liu parameter when the independent variable exhibits the multicollinearity problem. Full article
(This article belongs to the Special Issue Application of Regression Models, Analysis and Bayesian Statistics)
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17 pages, 428 KiB  
Article
Mitigating Multicollinearity in Regression: A Study on Improved Ridge Estimators
by Nadeem Akhtar, Muteb Faraj Alharthi and Muhammad Shakir Khan
Mathematics 2024, 12(19), 3027; https://doi.org/10.3390/math12193027 - 27 Sep 2024
Cited by 7 | Viewed by 2197
Abstract
Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): [...] Read more.
Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models. Full article
(This article belongs to the Special Issue Application of Regression Models, Analysis and Bayesian Statistics)
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16 pages, 860 KiB  
Article
Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application
by Adewale F. Lukman, Olayan Albalawi, Mohammad Arashi, Jeza Allohibi, Abdulmajeed Atiah Alharbi and Rasha A. Farghali
Mathematics 2024, 12(18), 2929; https://doi.org/10.3390/math12182929 - 20 Sep 2024
Cited by 3 | Viewed by 1760
Abstract
Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among [...] Read more.
Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among covariates and the presence of outliers can lead to inflated confidence intervals and inaccurate predictions in the model. This study proposes a comprehensive approach integrating robust and regularization techniques to handle the simultaneous impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We investigate the estimators’ performance through extensive simulation studies and provide analytical comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a forestry dataset. Our findings complement and reinforce the simulation and theoretical results. Full article
(This article belongs to the Special Issue Application of Regression Models, Analysis and Bayesian Statistics)
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