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Mathematics
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Statistics and Nonlinear Analysis: Simulation and Computation
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Statistics and Nonlinear Analysis: Simulation and Computation

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

Deadline for manuscript submissions: 30 September 2024 | Viewed by 1304

Special Issue Editor

Prof. Dr. Vesna Rajić

E-Mail Website
Guest Editor
Faculty of Economics and Business, University of Belgrade, Kamenička 6, Belgrade, Serbia
Interests: probability and statistics; nonlinear analysis; actuarial mathematics

Special Issue Information

Dear Colleagues,

In this Special Issue, we encourage submissions providing new results in the setting of statistics and nonlinear analysis and their applications.

Statistics and probability are important in many fields such as economy, sociology, psychology, forecasting, etc. Probability theory and distributions are used to define mathematical models in many branches of science. It is important to derive properties of distributions, estimate parameters, derive limit cases, or generalize results. Statistical research includes decision theory, estimation, hypothesis testing, large sample theory, asymptotic efficiency of estimators, exponential families, and sequential analysis. Statistical theory are also important in machine learning and big data science.

Nonlinear analysis is devoted to nonlinear problems from different areas. The purpose of this Special Issue is to gather significant contributions that concern fixed point theory and analysis of partial differential equations as well as their applications to nonlinear analysis and optimization. 

Prof. Dr. Vesna Rajić
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. 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

  • statistical inference
  • probability theory
  • distribution families
  • machine learning
  • statistical modeling
  • nonlinear analysis
  • fixed point theory
  • partial differential equations

Published Papers (2 papers)

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Research

24 pages, 3484 KiB  
Article
INLA Estimation of Semi-Variable Coefficient Spatial Lag Model—Analysis of PM2.5 Influencing Factors in the Context of Urbanization in China
by Qiong Pang and Xijian Hu
Mathematics 2024, 12(7), 953; https://doi.org/10.3390/math12070953 - 23 Mar 2024
Viewed by 405
Abstract
The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the “dimension disaster” associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, [...] Read more.
The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the “dimension disaster” associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, INLA is firstly used to estimate the parameters of (SVC-SLM) by using B-spline to deal with the non-parametric terms, and the comparative experimental results show that the INLA algorithm is much better than MCMCINLA in terms of both time efficiency and estimation accuracy. For the problem of identifying the constant coefficient terms in the SVC-SLM, the bootstrap test is given based on the residuals. Taking the PM2.5 data of 31 provinces in mainland China from 2015 to 2020 as an empirical example, parametric, non-parametric, and semi-parametric perspectives establish three models of Spatial Lag Model (SLM), VC-SLM, SVC-SLM, which explore the relationship between the covariate factors and the level of urbanization as well as their impacts on the concentration of PM2.5 in the context of increasing urbanization; among the three models, the SVC-SLM has the smallest values of DIC and WAIC, indicating that the SVC-SLM is optimal. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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14 pages, 1471 KiB  
Article
A Group MCP Approach for Structure Identification in Non-Parametric Accelerated Failure Time Additive Regression Model
by Sumin Hou and Hao Lv
Mathematics 2023, 11(22), 4628; https://doi.org/10.3390/math11224628 - 13 Nov 2023
Viewed by 613
Abstract
In biomedical research, identifying genes associated with diseases is of paramount importance. However, only a small fraction of genes are related to specific diseases among the multitude of genes. Therefore, gene selection and estimation are necessary, and the accelerated failure time model is [...] Read more.
In biomedical research, identifying genes associated with diseases is of paramount importance. However, only a small fraction of genes are related to specific diseases among the multitude of genes. Therefore, gene selection and estimation are necessary, and the accelerated failure time model is often used to address such issues. Hence, this article presents a method for structural identification and parameter estimation based on a non-parametric additive accelerated failure time model for censored data. Regularized estimation and variable selection are achieved using the Group MCP penalty method. The non-parametric component of the model is approximated using B-spline basis functions, and a group coordinate descent algorithm is employed for model solving. This approach effectively identifies both linear and nonlinear factors in the model. The Group MCP penalty estimation exhibits consistency and oracle properties under regularization conditions, meaning that the selected variable set tends to have a probability of approaching 1 and asymptotically includes the actual predictive factors. Numerical simulations and a lung cancer data analysis demonstrate that the Group MCP method outperforms the Group Lasso method in terms of predictive performance, with the proposed algorithm showing faster convergence rates. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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