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Axioms
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Computational Statistics and Its Applications
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Computational Statistics and Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 23 August 2024 | Viewed by 5181

Special Issue Editors

Prof. Dr. Eva T. López Sanjuán

E-Mail Website
Guest Editor
Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain
Interests: bayesian statistics; extreme value theory; applied statistics; ICT
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. María Isabel Parra Arévalo

E-Mail Website
Guest Editor
Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain
Interests: bayesian statistics; extreme value theory; applied statistics; ICT
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational statistics has become an essential basis for modern science in almost every field. Computational statistics uses algorithms and numerical methods to solve a multitude of problems, such as parameter estimation, hypothesis testing, and statistical modelling.

In this Special Issue, we are seeking high-quality research papers in areas of applied and computational statistics. Topics of interest include but are not limited to the following:

  • Probability theory;
  • Applied statistics;
  • Bayesian statistics;
  • Statistical analysis;
  • Multivariate statistics;
  • Regression models;
  • Statistical inference;
  • Sampling methods;
  • Statistics algorithms and software;
  • Digital technologies for statistics.

Prof. Dr. Eva T. López Sanjuán
Prof. Dr. María Isabel Parra Arévalo
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. Axioms 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 2400 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

  • applied statistics
  • Bayesian statistics
  • statistical analysis
  • regression models
  • statistical inference
  • likelihood-free inference
  • sampling methods
  • statistics algorithms and software
  • digital technologies for statistics

Published Papers (6 papers)

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Research

18 pages, 1306 KiB  
Article
Bayesian Inference for a Hidden Truncated Bivariate Exponential Distribution with Applications
by Indranil Ghosh, Hon Keung Tony Ng, Kipum Kim and Seong W. Kim
Axioms 2024, 13(3), 140; https://doi.org/10.3390/axioms13030140 - 22 Feb 2024
Viewed by 793
Abstract
In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data [...] Read more.
In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data when bivariate or multivariate observations are subject to some form of truncation. While the statistical inference for hidden truncation models (truncation from above) under the frequentist and the Bayesian paradigms has been adequately discussed in the literature, the estimation of a two-sided hidden truncation model under the Bayesian framework has not yet been discussed. In this paper, we consider the Bayesian inference for a general two-sided hidden truncation model based on the Arnold–Strauss bivariate exponential distribution. In addition, a Bayesian model selection approach based on the Bayes factor to select between models without truncation, with truncation from below, from above, and two-sided truncation is also explored. An extensive simulation study is carried out for varying parameter choices under the conjugate prior set-up. For illustrative purposes, a real-life dataset is re-analyzed to demonstrate the applicability of the proposed methodology. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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15 pages, 468 KiB  
Article
Bayesian Sensitivity Analysis for VaR and CVaR Employing Distorted Band Priors
by José Pablo Arias-Nicolás, María Isabel Parra, Mario M. Pizarro and Eva L. Sanjuán
Axioms 2024, 13(2), 77; https://doi.org/10.3390/axioms13020077 - 24 Jan 2024
Viewed by 737
Abstract
In the context of robust Bayesian analysis, studies mainly focus on computing the range of some quantities of interest when the prior distribution varies in a class. We use the concept of distorted bands to introduce a family of priors on the shape [...] Read more.
In the context of robust Bayesian analysis, studies mainly focus on computing the range of some quantities of interest when the prior distribution varies in a class. We use the concept of distorted bands to introduce a family of priors on the shape parameter of the Generalized Pareto distribution. We show how certain properties of the likelihood ratio order allow us to propose novel sensitivity measures for Value at Risk and Conditional Value at Risk, which are the most useful and reliable risk measures. Although we focus on the Generalized Pareto distribution, which is essential in Extreme Value Theory, the new sensitivity measures could be employed for all the distributions that verify certain conditions related to likelihood ratio order. A thorough simulation study was carried out to perform a sensitivity analysis, and two illustrative examples are also provided. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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22 pages, 359 KiB  
Article
Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model
by Mahmoud M. Abdelwahab, Mohamed R. Abonazel, Ali T. Hammad and Amera M. El-Masry
Axioms 2024, 13(1), 46; https://doi.org/10.3390/axioms13010046 - 11 Jan 2024
Viewed by 895
Abstract
This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus [...] Read more.
This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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13 pages, 1300 KiB  
Article
A Mixture Quantitative Randomized Response Model That Improves Trust in RRT Methodology
by Michael Parker, Sat Gupta and Sadia Khalil
Axioms 2024, 13(1), 11; https://doi.org/10.3390/axioms13010011 - 22 Dec 2023
Cited by 1 | Viewed by 816
Abstract
The Quantitative Randomized Response Technique (RRT) can be used by researchers to obtain honest answers to questions that, due to their sensitive (socially undesirable, dangerous, or even illegal) nature, might otherwise invoke partially or completely falsified responses. Over the years, Quantitative RRT models, [...] Read more.
The Quantitative Randomized Response Technique (RRT) can be used by researchers to obtain honest answers to questions that, due to their sensitive (socially undesirable, dangerous, or even illegal) nature, might otherwise invoke partially or completely falsified responses. Over the years, Quantitative RRT models, sometimes called Scrambling models, have been developed to incorporate such advancements as mixture, optionality and enhanced trust, each of which has important benefits. However, no single model incorporates all of these features. In this study, we propose just such a unified model, which we call the Mixture Optional Enhanced Trust (MOET) model. After developing methodologies to assess MOET based on standard approaches and using them to explore the key characteristics of the new model, we show that MOET has superior efficiency compared to the Quantitative Optional Enhanced Trust (OET) model. We also show that use of the model’s mixture capability allows practitioners to optimally balance the model’s efficiency with its privacy, making the model adaptable to a wide variety of research scenarios. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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18 pages, 1587 KiB  
Article
A Novel PM2.5 Concentration Forecasting Method Based on LFIG_DTW_HC Algorithm and Generalized Additive Model
by Hong Yang and Han Zhang
Axioms 2023, 12(12), 1118; https://doi.org/10.3390/axioms12121118 - 13 Dec 2023
Viewed by 834
Abstract
As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed [...] Read more.
As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed in this paper. First, take 30 provincial capitals in China for example, the cities are divided into seven regions by LFIG_DTW_HC algorithm, and descriptive statistics of PM2.5 concentration in each region are carried out. Secondly, it is found that the influencing factors of PM2.5 concentration are different in different regions. The input variables of the PM2.5 concentration forecasting model in each region are determined by combining the variable correlation with the generalized additive model, and the main influencing factors of PM2.5 concentration in each region are analyzed. Finally, the empirical analysis is conducted based on the input variables selected above, the generalized additive model is established to forecast PM2.5 concentration in each region, the comparison of the evaluation indexes of the training set and the test set proves that the novel PM2.5 concentration forecasting method achieves better prediction effect. Then, the generalized additive model is established by selecting cities from each region, and compared with the auto-regressive integrated moving average (ARIMA) model. The results show that the novel PM2.5 concentration forecasting method can achieve better prediction effect on the premise of ensuring high accuracy. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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12 pages, 301 KiB  
Article
Equation of Finite Change and Structural Analysis of Mean Value
by Stan Lipovetsky
Axioms 2023, 12(10), 962; https://doi.org/10.3390/axioms12100962 - 12 Oct 2023
Cited by 1 | Viewed by 718
Abstract
This paper describes a problem of finding the contributions of multiple variables to a change in their function. Such a problem is well known in economics, for example, in the decomposition of a change in the mean price via the varying in time [...] Read more.
This paper describes a problem of finding the contributions of multiple variables to a change in their function. Such a problem is well known in economics, for example, in the decomposition of a change in the mean price via the varying in time prices and volumes of multiple products. Commonly, it is considered by the tools of index analysis, the formulae of which present rather heuristic constructs. As shown in this work, the multivariate version of the Lagrange mean value theorem can be seen as an equation of the function’s finite change and solved with respect to an interior point whose value is used in the estimation of the contribution of the independent variables. Consideration is performed on the example of the weighted mean value function, which is the main characteristic of statistical estimation in various fields. The solution for this function can be obtained in the closed form, which helps in the analysis of results. Numerical examples include the cases of Simpson’s paradox, and practical applications are discussed. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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