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Mathematics
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Statistical Analysis: Theory, Methods and Applications
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Statistical Analysis: Theory, Methods and Applications

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

Deadline for manuscript submissions: closed (1 October 2024) | Viewed by 7494

Special Issue Editors

Dr. Laleh Tafakori

E-Mail Website
Guest Editor
Department of Mathematical Sciences, School of Science, RMIT University, Melbourne, VIC 3001, Australia
Interests: mathematical statistics; applied probability; extreme value theory; dependence modelling via copulas; time series; financial econometrics; stochastic processes
Prof. Dr. Marco Bee

E-Mail Website
Guest Editor
Department of Economics and Management, University of Trento, 38122 Trento, Italy
Interests: applied econometrics; computational statistics; loss models; Monte Carlo methods; quantitative risk management; statistical distributions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue on Statistical Analysis: Theory, Methods and Applications is a collection of articles that aims to present the recent advancements in statistical theory and methods, as well as their applications in various fields. The Issue covers a broad range of topics in statistics, including statistical extreme value theory, multivariate dependence modeling, Bayesian inference, nonparametric methods, statistical learning, time series analysis, and spatial statistics. The Special Issue includes articles that apply statistical methods to diverse application areas, such as healthcare, economics, environmental science, and social sciences. These applications highlight the importance of statistical analysis in understanding and solving real-world problems. Additionally, the Issue includes articles that address the challenges of working with complex data structures, such as time series data and high-dimensional data. Overall, the Special Issue provides a valuable resource for researchers and practitioners who are interested in the latest developments in statistical analysis and its applications. The articles in the Issue showcase the importance of statistical analysis in advancing scientific research and solving real-world problems.

Dr. Laleh Tafakori
Dr. Marco Bee
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

  • heavy-tailed phenomena and rare events
  • time series
  • multivariate dependence modeling
  • high-dimensional data analysis
  • statistical learning
  • spatial statistics
  • nonparametric methods
  • Bayesian statistics and modeling
  • causal inference
  • survival analysis

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Published Papers (6 papers)

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Research

25 pages, 6365 KiB  
Article
The Refinement of a Common Correlated Effect Estimator in Panel Unit Root Testing: An Extensive Simulation Study
by Tolga Omay, Yılmaz Akdi, Furkan Emirmahmutoglu and Meltem Eryılmaz
Mathematics 2024, 12(22), 3458; https://doi.org/10.3390/math12223458 - 5 Nov 2024
Viewed by 503
Abstract
The Common Correlated Effect (CCE) estimator is widely used in panel data models to address cross-sectional dependence, particularly in nonstationary panels. However, existing estimators have limitations, especially in small-sample settings. This study refines the CCE estimator by introducing new proxy variables and testing [...] Read more.
The Common Correlated Effect (CCE) estimator is widely used in panel data models to address cross-sectional dependence, particularly in nonstationary panels. However, existing estimators have limitations, especially in small-sample settings. This study refines the CCE estimator by introducing new proxy variables and testing them through a comprehensive set of simulations. The proposed method is simple yet effective, aiming to improve the handling of cross-sectional dependence. Simulation results show that the refined estimator eliminates cross-sectional dependence more effectively than the original CCE, with improved power properties under both weak- and strong-dependence scenarios. The refined estimator performs particularly well in small sample sizes. These findings offer a more robust framework for panel unit root testing, enhancing the reliability of CCE estimators and contributing to further developments in addressing cross-sectional dependence in panel data models. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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20 pages, 650 KiB  
Article
Approximately Optimal Domain Adaptation with Fisher’s Linear Discriminant
by Hayden Helm, Ashwin de Silva, Joshua T. Vogelstein, Carey E. Priebe and Weiwei Yang
Mathematics 2024, 12(5), 746; https://doi.org/10.3390/math12050746 - 1 Mar 2024
Viewed by 1062
Abstract
We propose and study a data-driven method that can interpolate between a classical and a modern approach to classification for a class of linear models. The class is the convex combinations of an average of the source task classifiers and a classifier trained [...] Read more.
We propose and study a data-driven method that can interpolate between a classical and a modern approach to classification for a class of linear models. The class is the convex combinations of an average of the source task classifiers and a classifier trained on the limited data available for the target task. We derive the expected loss of an element in the class with respect to the target distribution for a specific generative model, propose a computable approximation of the loss, and demonstrate that the element of the proposed class that minimizes the approximated risk is able to exploit a natural bias–variance trade-off in task space in both simulated and real-data settings. We conclude by discussing further applications, limitations, and potential future research directions. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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18 pages, 1420 KiB  
Article
Joint Statistics of Partial Sums of Ordered i.n.d. Gamma Random Variables
by Sung Sik Nam, Changseok Yoon and Seyeong Choi
Mathematics 2023, 11(20), 4273; https://doi.org/10.3390/math11204273 - 13 Oct 2023
Viewed by 982
Abstract
From the perspective of wireless communication, as communication systems become more complex, order statistics have gained increasing importance, particularly in evaluating the performance of advanced technologies in fading channels. However, existing analytical methods are often too complex for practical use. In this research [...] Read more.
From the perspective of wireless communication, as communication systems become more complex, order statistics have gained increasing importance, particularly in evaluating the performance of advanced technologies in fading channels. However, existing analytical methods are often too complex for practical use. In this research paper, we introduce innovative statistical findings concerning the sum of ordered gamma-distributed random variables. We examine various channel scenarios where these variables are independent but not-identically distributed. To demonstrate the practical applicability of our results, we provide a comprehensive closed-form expression for the statistics of the signal-to-interference-plus-noise ratio in a multiuser scheduling system. We also present numerical examples to illustrate the effectiveness of our approach. To ensure the accuracy of our analysis, we validate our analytical results through Monte Carlo simulations. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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28 pages, 514 KiB  
Article
Homogeneity Test for Multiple Semicontinuous Data with the Density Ratio Model
by Yufan Wang and Xingzhong Xu
Mathematics 2023, 11(17), 3789; https://doi.org/10.3390/math11173789 - 4 Sep 2023
Viewed by 956
Abstract
The density ratio model has been widely used in many research fields. To test the homogeneity of the model, the empirical likelihood ratio test (ELRT) has been shown to be valid. In this paper, we conduct a parametric test procedure. We transform the [...] Read more.
The density ratio model has been widely used in many research fields. To test the homogeneity of the model, the empirical likelihood ratio test (ELRT) has been shown to be valid. In this paper, we conduct a parametric test procedure. We transform the hypothesis of homogeneity to one on the equality of mean parameters of the exponential family of distributions. Then, we propose a modified Wald test and give its asymptotic power. We further apply it to the semicontinuous case when there is an excess of zeros in the sample. The simulation studies show that the new test controls the type-I error better than ELRT while retaining competitive power. Benefiting from the simple closed form of the test statistic, the computational cost is small. We also use a real data example to illustrate the effectiveness of our test. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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22 pages, 1938 KiB  
Article
Flexible-Elliptical Spatial Scan Method
by Mohammad Meysami, Joshua P. French and Ettie M. Lipner
Mathematics 2023, 11(17), 3627; https://doi.org/10.3390/math11173627 - 22 Aug 2023
Cited by 1 | Viewed by 1777
Abstract
The detection of disease clusters in spatial data analysis plays a crucial role in public health, while the circular scan method is widely utilized for this purpose, accurately identifying non-circular (irregular) clusters remains challenging and reduces detection accuracy. To overcome this limitation, various [...] Read more.
The detection of disease clusters in spatial data analysis plays a crucial role in public health, while the circular scan method is widely utilized for this purpose, accurately identifying non-circular (irregular) clusters remains challenging and reduces detection accuracy. To overcome this limitation, various extensions have been proposed to effectively detect arbitrarily shaped clusters. In this paper, we combine the strengths of two well-known methods, the flexible and elliptic scan methods, which are specifically designed for detecting irregularly shaped clusters. We leverage the unique characteristics of these methods to create candidate zones capable of accurately detecting irregularly shaped clusters, along with a modified likelihood ratio test statistic. By inheriting the advantages of the flexible and elliptic methods, our proposed approach represents a practical addition to the existing repertoire of spatial data analysis techniques. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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26 pages, 424 KiB  
Article
A New Instrumental-Type Estimator for Quantile Regression Models
by Li Tao, Lingnan Tai, Manling Qian and Maozai Tian
Mathematics 2023, 11(15), 3412; https://doi.org/10.3390/math11153412 - 4 Aug 2023
Cited by 1 | Viewed by 1236
Abstract
This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The [...] Read more.
This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures. Full article
(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)
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