Statistical Inference in Linear Models, 2nd Edition

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 31 December 2025 | Viewed by 469

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Center of Mathematics and Applications and Department of Mathematics, University of Beira Interior, 6201-001 Covilhã, Portugal
Interests: applied statistics; computational mathematical methods; distribution theory; linear models; prediction; statistical inference
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Special Issue Information

Dear Colleagues,

Linear models are very important statistical models that play a role in several fields of science, constituting an area of practical importance in statistics. The most typical variant is the linear regression model. Many phenomena, such as those seen in biology, medicine, economics, management, geology, meteorology, agriculture and industry, can be approximately described by linear models. The further research and development of linear models is still a very active research subject.

In this Special Issue, we invite front-line researchers and authors to submit novel and original research. Potential topics include, but are not limited to, the following areas:

  • Prediction and testing in linear models;
  • Regression and linear models;
  • Econometrics;
  • Robustness of relevant statistical methods;
  • Modelling and simulation;
  • Estimation of variance components;
  • Parameter estimation in linear models
  • Sampling techniques;
  • Applications of linear models;
  • Design and analysis of experiments;
  • Statistical applications;
  • Generalized linear models.

This collection of papers will reflect the state of the art in this area and present all recent important developments, providing a platform the benefit of young researchers coming into the field as well as seasoned researchers.

For further information, please send an email to sandraf@ubi.pt.

Dr. Sandra Ferreira
Guest Editor

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Keywords

  • linear models
  • regression models
  • parameter estimation
  • sampling

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Published Papers (1 paper)

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Research

33 pages, 3807 KiB  
Article
Statistical Modeling of Reliable Intervals for Solutions to Linear Transfer Problems Under Boundary Experimental Data
by Olha Chernukha, Petro Pukach, Yurii Bilushchak, Halyna Bilushchak and Myroslava Vovk
Math. Comput. Appl. 2025, 30(4), 89; https://doi.org/10.3390/mca30040089 - 12 Aug 2025
Viewed by 273
Abstract
A methodology for the statistical modeling of boundary value problems of mathematical physics for parabolic equations used to describe transport processes in a layer with incomplete data at the boundary of a body has been developed and presented. The boundary value problem is [...] Read more.
A methodology for the statistical modeling of boundary value problems of mathematical physics for parabolic equations used to describe transport processes in a layer with incomplete data at the boundary of a body has been developed and presented. The boundary value problem is formulated for the case of a non-zero initial condition, the presence of a stable source at one boundary of the body (classical boundary condition), and a sample of experimental data for the desired function at the other boundary (statistical boundary condition). A linear regression model obtained from experimental data by the least squares method is used as a boundary condition. The article defines two-sided statistical estimates of the solution of the boundary value problem through linear regression coefficients, analyzes the mathematical model taking into account the influence of the sample size and covariance, determines the reliable intervals for linear regression and the desired function depending on the given level of reliability. The influence of the experimental data statistical characteristics on the desired function at the lower layer’s boundary for different types of samples in the case of large or small-time intervals is studied. The two-sided critical domain is obtained and analyzed on the basis of Fisher’s criterion. The influence of the reliability level on the reliable intervals, the solution to the parabolic boundary value problem, and the width of the bilateral critical domain constructed for the solution is analyzed. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models, 2nd Edition)
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