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Stochastic Models and Statistical Inference: Analysis and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 4235

Special Issue Editors


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Guest Editor
Laboratoire de Mathématiques et Applications, University of Poitiers, 86000 Poitiers, France
Interests: nonparametric statistics; stochastic algorithms; statistics applied to life sciences; statistical learning of networks; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

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Assistant Guest Editor
Institut Montpelliérain Alexander Grothendieck, University Montpellier, CNRS, Montpellier, France
Interests: parameter estimation; stochastic model; stochastic model applied to life sciences; applied probability

Special Issue Information

Dear Colleagues,

Databases are becoming more and more accessible, voluminous and complex. In order to make the best use of them, non-parametric statistical methods, stochastic algorithms, statistical learning of networks, stochastic analysis are frequently used.

There has been growing increasing interest in Stochastic Models and Statistical Inference, including correlation analyses for spatial and temporal data and classification techniques for complex data. Progress has often been driven by the application areas, such as neurosciences, environmetrics, chemometrics, biometrics, medicine, and econometrics.

The application of Stochastic Models and Statistical Inference to data of real-world complex systems are often hindered by the frequent lack of the convergence problems and sufficient asymptotic mathematical properties. Contributions addressing any of these issues are very welcome.

This Special Issue aims to be a forum for the presentation of new and improved techniques in the area of Stochastic Models and Statistical Inference. In particular, the analysis and interpretation of real-world natural and engineered complex systems with the help of non-parametric statistical methods, stochastic algorithms, statistical learning of networks, Stochastic Models fall within the scope of this Special Issue as well as parameter estimation.

Dr. Yousri Slaoui
Dr. Solym Mawaki Manou-Abi
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. Entropy 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 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

  • stochastic model
  • parameter estimation
  • data analysis
  • stochastic algorithms
  • simulation

Published Papers (4 papers)

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Research

13 pages, 539 KiB  
Article
Estimation of a Simple Structure in a Multidimensional IRT Model Using Structure Regularization
by Ryosuke Shimmura and Joe Suzuki
Entropy 2024, 26(1), 44; https://doi.org/10.3390/e26010044 - 31 Dec 2023
Viewed by 796
Abstract
We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items [...] Read more.
We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent traits. The basic idea of our approach is to use the prenet (product-based elastic net) penalty, as proposed in factor analysis. For optimization, we show that combining stochastic EM algorithms, proximal gradient methods, and coordinate descent methods efficiently yields solutions. Furthermore, our numerical experiments demonstrate its effectiveness, especially in cases where the number of test subjects is small, compared to methods using the existing L1 penalty. Full article
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14 pages, 770 KiB  
Article
Bridging Extremes: The Invertible Bimodal Gumbel Distribution
by Cira G. Otiniano, Eduarda B. Silva, Raul Y. Matsushita and Alan Silva
Entropy 2023, 25(12), 1598; https://doi.org/10.3390/e25121598 - 29 Nov 2023
Viewed by 696
Abstract
This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in [...] Read more.
This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously. Full article
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13 pages, 1184 KiB  
Article
Gaussian and Lerch Models for Unimodal Time Series Forcasting
by Azzouz Dermoune, Daoud Ounaissi and Yousri Slaoui
Entropy 2023, 25(10), 1474; https://doi.org/10.3390/e25101474 - 22 Oct 2023
Viewed by 985
Abstract
We consider unimodal time series forecasting. We propose Gaussian and Lerch models for this forecasting problem. The Gaussian model depends on three parameters and the Lerch model depends on four parameters. We estimate the unknown parameters by minimizing the sum of the absolute [...] Read more.
We consider unimodal time series forecasting. We propose Gaussian and Lerch models for this forecasting problem. The Gaussian model depends on three parameters and the Lerch model depends on four parameters. We estimate the unknown parameters by minimizing the sum of the absolute values of the residuals. We solve these minimizations with and without a weighted median and we compare both approaches. As a numerical application, we consider the daily infections of COVID-19 in China using the Gaussian and Lerch models. We derive a confident interval for the daily infections from each local minima. Full article
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33 pages, 804 KiB  
Article
Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data
by Ouahiba Litimein, Fatimah Alshahrani, Salim Bouzebda, Ali Laksaci and Boubaker Mechab
Entropy 2023, 25(7), 1108; https://doi.org/10.3390/e25071108 - 24 Jul 2023
Viewed by 805
Abstract
The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is [...] Read more.
The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is a fundamental tool in characterizing the convergence rate of the local linear estimation. Precisely, we use this tool to derive the uniform convergence rate of the local linear estimation of the conditional cumulative distribution function and the local linear estimation conditional quantile function. Second, a central limit theorem for the proposed estimators is established. These results are proved under general assumptions, allowing for the incomplete functional time series case to be covered. Specifically, we model the correlation using the ergodic assumption and assume that the response variable is collected with missing at random. Finally, we conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimators. Full article
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