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Mathematics
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Computational Statistical Methods and Extreme Value Theory
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Computational Statistical Methods and Extreme Value Theory

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 19037

Special Issue Editor

Prof. Dr. Frederico Caeiro

E-Mail Website
Guest Editor
Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa Quinta da Torre, 2829-516 Caparica, Portugal
Interests: applications of statistics of extreme values in risk management; computational statistical methods; probability distribution theory; extreme value theory; non-parametric statistics; statistics of extremes

Special Issue Information

Dear Colleagues,

In the last decades, computers’ power has increased exponentially and has allowed the rise of new and more complex computationally intensive statistical methods. Among these, we may mention, for example, computational algorithms, computational Bayesian methods, data mining, high-dimensional data analysis, machine learning, Monte Carlo simulation, multivariate data analysis, resampling, statistical learning, and stochastic optimization.

Another subject that has gained considerable importance in the past few decades is the Extreme Value Theory. This discipline provides the adequate methodology for the prediction of extreme and rare events, that is, events that occur irregularly with a small probability. We can find applications of the Extreme Value Theory is several fields, such as biostatistics, engineering, finance, geology, hydrology, insurance, meteorology, and public health.

The purpose of this Special Issue is to provide a collection of articles that reflect the latest developments in the fields of Computational Statistical Methods and Extreme Value Theory. Papers providing new methodologies and applications regarding the aforementioned topics are welcome.

Prof. Dr. Frederico Caeiro
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

  • Computational algorithms
  • Data analysis
  • Data mining
  • Extreme Value Theory
  • Monte Carlo Simulation
  • Resampling
  • Statistics of Extremes

Published Papers (6 papers)

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Research

17 pages, 459 KiB  
Article
Scale Mixture of Exponential Distribution with an Application
by Jorge A. Barahona, Yolanda M. Gómez, Emilio Gómez-Déniz, Osvaldo Venegas and Héctor W. Gómez
Mathematics 2024, 12(1), 156; https://doi.org/10.3390/math12010156 - 3 Jan 2024
Viewed by 655
Abstract
This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis [...] Read more.
This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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17 pages, 367 KiB  
Article
A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution
by Frederico Caeiro and Ayana Mateus
Mathematics 2023, 11(5), 1076; https://doi.org/10.3390/math11051076 - 21 Feb 2023
Cited by 1 | Viewed by 1237
Abstract
Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of [...] Read more.
Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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30 pages, 19554 KiB  
Article
On a Parallelised Diffusion Induced Stochastic Algorithm with Pure Random Search Steps for Global Optimisation
by Manuel L. Esquível, Nadezhda P. Krasii, Pedro P. Mota and Nélio Machado
Mathematics 2021, 9(23), 3043; https://doi.org/10.3390/math9233043 - 26 Nov 2021
Viewed by 1466
Abstract
We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion [...] Read more.
We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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13 pages, 1876 KiB  
Article
Greening the Financial System in USA, Canada and Brazil: A Panel Data Analysis
by Ioan Batrancea, Larissa Batrancea, Malar Maran Rathnaswamy, Horia Tulai, Gheorghe Fatacean and Mircea-Iosif Rus
Mathematics 2020, 8(12), 2217; https://doi.org/10.3390/math8122217 - 14 Dec 2020
Cited by 50 | Viewed by 5055
Abstract
Each country designs its own scheme to achieve green financing and, in general, credit is considered to be a fundamental source of greening financial systems. The novelty of this study resides in that we examined green financing initiatives in USA, Canada and Brazil [...] Read more.
Each country designs its own scheme to achieve green financing and, in general, credit is considered to be a fundamental source of greening financial systems. The novelty of this study resides in that we examined green financing initiatives in USA, Canada and Brazil by focusing on major components of the financial systems before, during and after the 2008 world financial crisis. By means of panel data analysis conducted on observations ranging across the period 1970–2018, we investigated variables such as domestic credit from banks, domestic credit from the financial sector, GDP, N2O emissions, CO2 emissions and the value added from agriculture, forest and fishing activities. According to our findings, domestic credit from banks was insufficient to achieve green financing. Namely, in order to increase economic growth while reducing global warming and climate change, the financial sector should assume a bigger role in funding green investments. Moreover, our results showed that domestic credit from the financial sector contributed to green financing, while CO2 emissions remained a challenge in capping global warming at the 1.5 °C level. Our empirical study supports the idea that economic growth together with policies targeting climate change and global warming can contribute to green financing. Over and above that, governments should strive to design sustainable fiscal and monetary policies that promote green financing. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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22 pages, 2489 KiB  
Article
Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution
by Palakorn Seenoi, Piyapatr Busababodhin and Jeong-Soo Park
Mathematics 2020, 8(12), 2180; https://doi.org/10.3390/math8122180 - 7 Dec 2020
Cited by 6 | Viewed by 2385
Abstract
Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained [...] Read more.
Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained by virtue of a posterior distribution using the random walk Metropolis–Hastings algorithm. Five different priors are considered. The properties of the Bayesian estimators are verified in a simulation study. The empirical Bayesian method turns out to work well. Our approach is then compared to the MLE and the method of the L-moments estimator by calculating the 20-year return level, the confidence interval, and various goodness-of-fit measures. It is also compared to modeling using the generalized extreme value distribution. We illustrate the usefulness of our approach in an application to the annual maximum wind speeds in Udon Thani, Thailand, and to the annual maximum sea-levels in Fremantle, Australia. In the latter example, non-stationarity is modeled through a trend in time on the location parameter. We conclude that Bayesian inference for K4D may be substantially useful for modeling extreme events. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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24 pages, 1364 KiB  
Article
Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection
by Krzysztof Echaust and Małgorzata Just
Mathematics 2020, 8(1), 114; https://doi.org/10.3390/math8010114 - 11 Jan 2020
Cited by 19 | Viewed by 6350
Abstract
A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate [...] Read more.
A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold. Full article
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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