Stats

27 pages, 677 KiB

Open AccessArticle

Optimal ANOVA-Based Emulators of Models With(out) Derivatives

by Matieyendou Lamboni

Stats 2025, 8(1), 24; https://doi.org/10.3390/stats8010024 - 17 Mar 2025

This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, [...] Read more.

This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, our derivative-based emulators reach dimension-free mean squared errors (MSEs) and a parametric rate of convergence (i.e.,

O (N^{- 1})

). This approach is extended to cope with every model (without available derivatives) by deriving global emulators that account for the local properties of models or simulators. Such generic emulators enjoy dimension-free biases, parametric rates of convergence, and MSEs that depend on the dimensionality. Dimension-free MSEs are obtained for high-dimensional models with particular distributions from the input. Our emulators are also competitive in dealing with different distributions of the input variables and selecting inputs and interactions. Simulations show the efficiency of our approach. Full article

(This article belongs to the Section Statistical Methods)

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7 pages, 207 KiB

Open AccessArticle

Statistical Gravity and Entropy of Spacetime

by Riccardo Fantoni

Stats 2025, 8(1), 23; https://doi.org/10.3390/stats8010023 - 13 Mar 2025

Abstract

We discuss the foundations of the statistical gravity theory we proposed in a recent publication [Riccardo Fantoni, Quantum Reports, 6, 706 (2024)]. Full article

25 pages, 400 KiB

Open AccessArticle

A Flexible Bivariate Integer-Valued Autoregressive of Order (1) Model for Over- and Under-Dispersed Time Series Applications

by Naushad Mamode Khan and Yuvraj Sunecher

Stats 2025, 8(1), 22; https://doi.org/10.3390/stats8010022 - 12 Mar 2025

Abstract

In real-life inter-related time series, the counting responses of different entities are commonly influenced by some time-dependent covariates, while the individual counting series may exhibit different levels of mutual over- or under-dispersion or mixed levels of over- and under-dispersion. In the current literature, [...] Read more.

In real-life inter-related time series, the counting responses of different entities are commonly influenced by some time-dependent covariates, while the individual counting series may exhibit different levels of mutual over- or under-dispersion or mixed levels of over- and under-dispersion. In the current literature, there is still no flexible bivariate time series process that can model series of data of such types. This paper introduces a bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with COM-Poisson innovations under time-dependent moments that can accommodate different levels of over- and under-dispersion. Another particularity of the proposed model is that the cross-correlation between the series is induced locally by relating the current observation of one series with the previous-lagged observation of the other series. The estimation of the model parameters is conducted via a Generalized Quasi-Likelihood (GQL) approach. The proposed model is applied to different real-life series problems in Mauritius, including transport, finance, and socio-economic sectors. Full article

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9 pages, 965 KiB

Open AccessCommunication

The Gamma-G Family: Brief Survey and COVID-19 Application

by Gauss M. Cordeiro and Alexsandro A. Ferreira

Stats 2025, 8(1), 21; https://doi.org/10.3390/stats8010021 - 5 Mar 2025

Abstract

In recent years, the gamma-G family has gained significant popularity for generating new distributions by incorporating an additional shape parameter into the baseline model. This article compiles and documents the existing gamma-G distributions and demonstrates their application to real COVID-19 data. Full article

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24 pages, 326 KiB

Open AccessArticle

Quantum-Inspired Latent Variable Modeling in Multivariate Analysis

by Theodoros Kyriazos and Mary Poga

Stats 2025, 8(1), 20; https://doi.org/10.3390/stats8010020 - 28 Feb 2025

Abstract

Latent variables play a crucial role in psychometric research, yet traditional models often struggle to address context-dependent effects, ambivalent states, and non-commutative measurement processes. This study proposes a quantum-inspired framework for latent variable modeling that employs Hilbert space representations, allowing questionnaire items to [...] Read more.

Latent variables play a crucial role in psychometric research, yet traditional models often struggle to address context-dependent effects, ambivalent states, and non-commutative measurement processes. This study proposes a quantum-inspired framework for latent variable modeling that employs Hilbert space representations, allowing questionnaire items to be treated as pure or mixed quantum states. By integrating concepts such as superposition, interference, and non-commutative probabilities, the framework captures cognitive and behavioral phenomena that extend beyond the capabilities of classical methods. To illustrate its potential, we introduce quantum-specific metrics—fidelity, overlap, and von Neumann entropy—as complements to correlation-based measures. We also outline a machine-learning pipeline using complex and real-valued neural networks to handle amplitude and phase information. Results highlight the capacity of quantum-inspired models to reveal order effects, ambivalent responses, and multimodal distributions that remain elusive in standard psychometric approaches. This framework broadens the multivariate analysis theoretical and methodological toolkit, offering a dynamic and context-sensitive perspective on latent constructs while inviting further empirical validation in diverse research settings. Full article

(This article belongs to the Section Multivariate Analysis)

37 pages, 14387 KiB

Open AccessArticle

Deviations from Normality in Autocorrelation Functions and Their Implications for MA(q) Modeling

by Manuela Royer-Carenzi and Hossein Hassani

Stats 2025, 8(1), 19; https://doi.org/10.3390/stats8010019 - 20 Feb 2025

Abstract

The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for [...] Read more.

The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for lags beyond q. This property is widely used in model selection, assuming the sample ACF follows an asymptotic normal distribution for robustness. However, our examination of the sum of the sample ACF reveals inconsistencies with these theoretical properties, highlighting a deviation from normality in the sample ACF for MA(q) processes. As a natural extension of the ACF, the Extended Autocorrelation Function (EACF) provides additional insights by facilitating the simultaneous identification of both autoregressive and moving average components. Using simulations, we evaluate the performance of q-order identification in MA(q) models, which is based on the properties of ACF. Similarly, for ARMA(

p, q

) models, we assess the (

p, q

)-order identification relying on EACF. Our findings indicate that both methods are effective for sufficiently long time series but may incorrectly favor an ARMA(

p, q - 1

) model when the

a_{q}

coefficient approaches zero. Additionally, if the cumulative sums of ACF (SACF) behave consistently and the Ljung–Box test validates the proposed model, it can serve as a strong candidate. The proposed models should then be compared based on their predictive performance. We illustrate our methodology with an application to wind speed data and sea surface temperature anomalies, providing practical insights into the relevance of our findings. Full article

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9 pages, 965 KiB

Open AccessCommunication

STATom@ic: R Package for Automated Statistical Analysis of Omic Datasets

by Rui S. Treves, Tyler C. Gripshover and Josiah E. Hardesty

Stats 2025, 8(1), 18; https://doi.org/10.3390/stats8010018 - 11 Feb 2025

Abstract

Background: The evolution of “omic” technologies, which measure all biological molecules of a specific type (e.g., genomics), has enabled rapid and cost-effective data acquisition, depending on the technique and sample size. This, however, generates new hurdles that need to be addressed and should [...] Read more.

Background: The evolution of “omic” technologies, which measure all biological molecules of a specific type (e.g., genomics), has enabled rapid and cost-effective data acquisition, depending on the technique and sample size. This, however, generates new hurdles that need to be addressed and should be improved upon. This includes selecting the appropriate statistical test based on study design in a high-throughput manner. Methods: An automated statistical analysis pipeline for omic datasets that we coined STATom@ic (pronounced stat-o-matic) was developed in R programming language. Results: We developed an R package that enables statisticians, bioinformaticians, and scientists to perform assumption tests (e.g., normality and variance homogeneity) before selecting appropriate statistical tests. This analysis package can handle two-group and multiple-group comparisons. In addition, this R package can be used for many data formats including normalized counts (RNASeq) and spectral abundance (proteomics and metabolomics). STATom@ic has high precision but lower recall compared to DeSeq2. Conclusions: The STATom@ic R Package is a user-friendly stand-alone or add-on to current bioinformatic workflows that automatically performs appropriate statistical analysis based on the characteristics of the data. Full article

(This article belongs to the Section Biostatistics)

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13 pages, 489 KiB

Open AccessArticle

Limits of Agreement Based on Transformed Measurements

by Erik Thorlund Parner

Stats 2025, 8(1), 17; https://doi.org/10.3390/stats8010017 - 10 Feb 2025

Abstract

Method comparison studies are typically analyzed using limits of agreement (LoAs). The standard Bland–Altman approach estimates LoAs under the assumption that the differences between methods follow a normal distribution. However, many types of measurements, such as volume, concentration, and percentage values, often deviate [...] Read more.

Method comparison studies are typically analyzed using limits of agreement (LoAs). The standard Bland–Altman approach estimates LoAs under the assumption that the differences between methods follow a normal distribution. However, many types of measurements, such as volume, concentration, and percentage values, often deviate from normality. This study explores LoAs for the difference between two clinical measurements and prediction intervals for one measurement given the other, using a transformation of the data. After back-transforming, the resulting LoA for the original measurements depends on the subject level, represented by the average of the measurements. A simulation study evaluates the statistical properties of these LoAs and their confidence limits, demonstrating strong performance for small-to-medium sample sizes. LoA derived from transformed measurements are also compared with those obtained using a regression-based method proposed by Bland and Altman. Two applications demonstrate the approach using logarithmic and cube root transformations. This transformation-based method offers a straightforward way to obtain LoAs that depends on the subject level. Full article

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33 pages, 878 KiB

Open AccessArticle

An Unbiased Convex Estimator Depending on Prior Information for the Classical Linear Regression Model

by Mustafa I. Alheety, HM Nayem and B. M. Golam Kibria

Stats 2025, 8(1), 16; https://doi.org/10.3390/stats8010016 - 9 Feb 2025

Abstract

We propose an unbiased restricted estimator that leverages prior information to enhance estimation efficiency for the linear regression model. The statistical properties of the proposed estimator are rigorously examined, highlighting its superiority over several existing methods. A simulation study is conducted to evaluate [...] Read more.

We propose an unbiased restricted estimator that leverages prior information to enhance estimation efficiency for the linear regression model. The statistical properties of the proposed estimator are rigorously examined, highlighting its superiority over several existing methods. A simulation study is conducted to evaluate the performance of the estimators, and real-world data on total national research and development expenditures by country are analyzed to illustrate the findings. Both the simulation results and real-data analysis demonstrate that the proposed estimator consistently outperforms the alternatives considered in this study. Full article

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17 pages, 564 KiB

Open AccessCommunication

Note on Pre-Taxation Data Reported by UK FTSE-Listed Companies: Search for Compatibility with Benford’s Laws

by Marcel Ausloos, Probowo Erawan Sastroredjo and Polina Khrennikova

Stats 2025, 8(1), 15; https://doi.org/10.3390/stats8010015 - 7 Feb 2025

Abstract

Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income (

P I

) [...] Read more.

Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income (

P I

) and total assets (

T A

) data from 567 companies listed on the FTSE All-Share index, gathered from the Refinitiv EIKON database, covering 14 years, i.e., the period from 2009 to 2022. We also derive the

P I / T A

ratio, and distinguish between positive and negative

P I

cases. We test the conformity of such data to Benford’s Laws, specifically studying the first significant digit (

F d

), the second significant digit (

S d

), and the first and second significant digits (

F S d

). We use and justify two pertinent tests, the

χ^{2}

and the Mean Absolute Deviation (MAD). We find that both tests do not lead to conclusions in complete agreement with each other—in particular, the MAD test entirely rejects the Benford’s Laws conformity of the reported financial data. From the mere accounting point of view, we conclude that the findings not only cast some doubt on the reported financial data, but also suggest that many more investigations should be considered on closely related matters. On the other hand, the study of a ratio, like

P I / T A

, of variables that are (or are not) Benford’s Laws-compliant adds to the literature concerning whether such indirect variables should (or should not) be Benford’s Laws-compliant. Full article

(This article belongs to the Section Financial Statistics)

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23 pages, 1253 KiB

Open AccessArticle

EEG Signal Analysis for Numerical Digit Classification: Methodologies and Challenges

by Augoustos Tsamourgelis and Adam Adamopoulos

Stats 2025, 8(1), 14; https://doi.org/10.3390/stats8010014 - 5 Feb 2025

Abstract

Electroencephalography (EEG) has existed since the early 20th century. It has proven to be a vital tool for electrophysiological studies of conditions like epilepsy. Recently, it has been revitalized as the field of machine learning has been developing, widening its usefulness among a [...] Read more.

Electroencephalography (EEG) has existed since the early 20th century. It has proven to be a vital tool for electrophysiological studies of conditions like epilepsy. Recently, it has been revitalized as the field of machine learning has been developing, widening its usefulness among a plethora of neurological conditions and in brain–computer interface (BCI) applications. This study delves into the intricate process of classifying EEG signals elicited by the visual stimuli of subjects viewing the digits 0 and 1 and a blank screen. We focus on developing a comprehensive workflow for EEG preprocessing, as well as feature extraction and signal classification. We achieve strong differentiation capabilities between digit and non-digit values in all classification algorithms. However, our study also highlights the profound neurological challenges encountered in distinguishing between the digit values, as our model, inspired by the related bibliography, was unable to differentiate between digit values 0 and 1. These findings underscore the complexity of numerical processing in the brain, revealing critical insights into the limitations and potential of EEG-based digit classification and the need for clarity in the bioinformatics community. Full article

(This article belongs to the Section Time Series Analysis)

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26 pages, 12220 KiB

Open AccessArticle

Measurement and Decomposition Analysis of Occupational Income Inequality in China

by Jing Yuan, Teng Ma, Yinghui Wang and Zongwu Cai

Stats 2025, 8(1), 13; https://doi.org/10.3390/stats8010013 - 2 Feb 2025

Abstract

Using the China CFPS database, this paper measures the degree of intra-occupational inequality in China with the Pareto coefficient and uses the generalized entropy index to decompose the top income gap by region as well as by industry. The empirical results show that, [...] Read more.

Using the China CFPS database, this paper measures the degree of intra-occupational inequality in China with the Pareto coefficient and uses the generalized entropy index to decompose the top income gap by region as well as by industry. The empirical results show that, firstly, the degree of income inequality between occupations in China has increased significantly in recent years. The provinces with a higher degree of income inequality between occupations are mostly located in the more economically developed regions in the central and eastern parts of the country, while the degree of inequality between occupations in the western part is lower. Secondly, the highest-income occupations are mainly in the manufacturing industry, with relatively high levels in the construction industry, the education sector, the wholesale and retail trade, and public administration and social organizations, while the levels in other occupations are relatively low. Lastly, the top income gap primarily originates from within industries. However, the contribution rate of the top income gap between industries is gradually increasing, while the contribution rate of the top income gap within industries is gradually decreasing. Full article

(This article belongs to the Section Financial Statistics)

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17 pages, 1319 KiB

Open AccessCommunication

Smart Renting: Harnessing Urban Data with Statistical and Machine Learning Methods for Predicting Property Rental Prices from a Tenant’s Perspective

by Francisco Louzada, Kleython José Coriolano Cavalcanti de Lacerda, Paulo Henrique Ferreira and Naomy Duarte Gomes

Stats 2025, 8(1), 12; https://doi.org/10.3390/stats8010012 - 27 Jan 2025

Abstract

The real estate market plays a pivotal role in most nations’ economy, showcasing continuous growth. Particularly noteworthy is the rapid expansion of the digital real estate sector, marked by innovations like 3D visualization and streamlined online contractual processes, a momentum further accelerated by [...] Read more.

The real estate market plays a pivotal role in most nations’ economy, showcasing continuous growth. Particularly noteworthy is the rapid expansion of the digital real estate sector, marked by innovations like 3D visualization and streamlined online contractual processes, a momentum further accelerated by the aftermath of the Coronavirus Disease 2019 (COVID-19) pandemic. Amidst this transformative landscape, artificial intelligence emerges as a vital force, addressing consumer needs by harnessing data analytics for predicting and monitoring rental prices. While studies have demonstrated the efficacy of machine learning (ML) algorithms such as decision trees and neural networks in predicting house prices, there is a lack of research specifically focused on rental property prices, a significant sector in Brazil due to the prohibitive costs associated with property acquisition. This study fills this crucial gap by delving into the intricacies of rental pricing, using data from the city of São Carlos-SP, Brazil. The research aims to analyze, model, and predict rental prices, employing an approach that incorporates diverse ML models. Through this analysis, our work showcases the potential of ML algorithms in accurately predicting rental house prices. Moreover, it envisions the practical application of this research with the development of a user-friendly website. This platform could revolutionize the renting experience, empowering both tenants and real estate agencies with the ability to estimate rental values based on specific property attributes and have access to its statistics. Full article

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32 pages, 3452 KiB

Open AccessReview

Assessment of Reliability Allocation Methods for Electronic Systems: A Systematic and Bibliometric Analysis

by Rajkumar B. Patil, San Kyeong, Michael Pecht, Rahul A. Gujar and Sandip Mane

Stats 2025, 8(1), 11; https://doi.org/10.3390/stats8010011 - 24 Jan 2025

Abstract

Reliability allocation is the process of assigning reliability targets to sub-systems within a system to meet the overall reliability requirements. However, many traditional reliability allocation methods rely on assumptions that are often unrealistic, leading to misleading, unachievable, and costly outcomes. This paper provides [...] Read more.

Reliability allocation is the process of assigning reliability targets to sub-systems within a system to meet the overall reliability requirements. However, many traditional reliability allocation methods rely on assumptions that are often unrealistic, leading to misleading, unachievable, and costly outcomes. This paper provides a historical review of reliability allocation methods, focusing on the Weighing Factor Method (WFM), with a detailed analysis of its main findings, assumptions, and limitations. Additionally, the review covers methods for reliability optimization, redundancy optimization, and multi-state system optimization, highlighting their strengths and shortcomings. A case study is presented to demonstrate how the assumption of an exponential distribution impacts the reliability allocation process, showing the limitations it imposes on practical implementations. Furthermore, a bibliometric analysis is conducted to assess publication trends in the field of reliability allocation. Through examples, particularly in the context of electronic systems using commercial off-the-shelf (COTS) components, the challenges are discussed, and recommendations for alternative approaches to improve the reliability allocation process are provided. Full article

(This article belongs to the Section Reliability Engineering)

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35 pages, 8999 KiB

Open AccessArticle

An Improved Soft Island Model of the Fish School Search Algorithm with Exponential Step Decay Using Cluster-Based Population Initialization

by Liliya A. Demidova and Vladimir E. Zhuravlev

Stats 2025, 8(1), 10; https://doi.org/10.3390/stats8010010 - 22 Jan 2025

Abstract

Optimization is a highly relevant area of research due to its widespread applications. The development of new optimization algorithms or the improvement of existing ones enhances the efficiency of various fields of activity. In this paper, an improved Soft Island Model (SIM) is [...] Read more.

Optimization is a highly relevant area of research due to its widespread applications. The development of new optimization algorithms or the improvement of existing ones enhances the efficiency of various fields of activity. In this paper, an improved Soft Island Model (SIM) is considered for the Tent-map-based Fish School Search algorithm with Exponential step decay (ETFSS). The proposed model is based on a probabilistic approach to realize the migration process relying on the statistics of the overall achievement of each island. In order to generate the initial population of the algorithm, a new initialization method is proposed in which all islands are formed in separate regions of the search space, thus forming clusters. For the presented SIM-ETFSS algorithm, numerical experiments with the optimization of classical test functions, as well as checks for the presence of some known defects that lead to undesirable effects in problem solving, have been carried out. Tools, such as the Mann–Whitney U test, box plots and other statistical methods of data analysis, are used to evaluate the quality of the presented algorithm, using which the superiority of SIM-ETFSS over its original version is demonstrated. The results obtained are analyzed and discussed. Full article

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20 pages, 1008 KiB

Open AccessArticle

Predicting and Mitigating Delays in Cross-Dock Operations: A Data-Driven Approach

by Amna Altaf, Adeel Mehmood, Adnen El Amraoui, François Delmotte and Christophe Lecoutre

Stats 2025, 8(1), 9; https://doi.org/10.3390/stats8010009 - 20 Jan 2025

Abstract

Cross-docking operations are highly dependent on precise scheduling and timely truck arrivals to ensure streamlined logistics and minimal storage costs. Predicting potential delays in truck arrivals is essential to avoiding disruptions that can propagate throughout the cross-dock facility. This paper investigates the effectiveness [...] Read more.

Cross-docking operations are highly dependent on precise scheduling and timely truck arrivals to ensure streamlined logistics and minimal storage costs. Predicting potential delays in truck arrivals is essential to avoiding disruptions that can propagate throughout the cross-dock facility. This paper investigates the effectiveness of deep learning models, including Convolutional Neural Networks (CNN), Multilayer Perceptrons (MLPs), and Recurrent Neural Networks (RNNs), in predicting late arrivals of trucks. Through extensive comparative analysis, we evaluate the performance of each model in terms of prediction accuracy and applicability to real-world cross-docking requirements. The results highlight which models can most accurately predict delays, enabling proactive measures for handling deviations and improving operational efficiency. Our findings support the potential for deep learning models to enhance cross-docking reliability, ultimately contributing to optimized logistics and supply chain resilience. Full article

(This article belongs to the Section Reliability Engineering)

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20 pages, 3127 KiB

Open AccessArticle

A New Weighted Lindley Model with Applications to Extreme Historical Insurance Claims

by Morad Alizadeh, Mahmoud Afshari, Gauss M. Cordeiro, Ziaurrahman Ramaki, Javier E. Contreras-Reyes, Fatemeh Dirnik and Haitham M. Yousof

Stats 2025, 8(1), 8; https://doi.org/10.3390/stats8010008 - 15 Jan 2025

Abstract

In this paper, we propose a weighted Lindley (NWLi) model for the analysis of extreme historical insurance claims. It extends the classical Lindley distribution by incorporating a weight parameter, enabling more flexibility in modeling insurance claim severity. We provide a comprehensive theoretical overview [...] Read more.

In this paper, we propose a weighted Lindley (NWLi) model for the analysis of extreme historical insurance claims. It extends the classical Lindley distribution by incorporating a weight parameter, enabling more flexibility in modeling insurance claim severity. We provide a comprehensive theoretical overview of the new model and explore two practical applications. First, we investigate the mean-of-order P (MOOP_(P)) approach for quantifying the expected claim severity based on the NWLi model. Second, we implement a peaks over a random threshold (PORT) analysis using the value-at-risk metric to assess extreme claim occurrences under the new model. Further, we provide a simulation study to evaluate the accuracy of the estimators under various methods. The proposed model and its applications provide a versatile tool for actuaries and risk analysts to analyze and predict extreme insurance claim severity, offering insights into risk management and decision-making within the insurance industry. Full article

(This article belongs to the Section Reliability Engineering)

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18 pages, 1035 KiB

Open AccessArticle

Bidirectional f-Divergence-Based Deep Generative Method for Imputing Missing Values in Time-Series Data

by Wen-Shan Liu, Tong Si, Aldas Kriauciunas, Marcus Snell and Haijun Gong

Stats 2025, 8(1), 7; https://doi.org/10.3390/stats8010007 - 14 Jan 2025

Cited by 1

Abstract

Imputing missing values in high-dimensional time-series data remains a significant challenge in statistics and machine learning. Although various methods have been proposed in recent years, many struggle with limitations and reduced accuracy, particularly when the missing rate is high. In this work, we [...] Read more.

Imputing missing values in high-dimensional time-series data remains a significant challenge in statistics and machine learning. Although various methods have been proposed in recent years, many struggle with limitations and reduced accuracy, particularly when the missing rate is high. In this work, we present a novel f-divergence-based bidirectional generative adversarial imputation network, tf-BiGAIN, designed to address these challenges in time-series data imputation. Unlike traditional imputation methods, tf-BiGAIN employs a generative model to synthesize missing values without relying on distributional assumptions. The imputation process is achieved by training two neural networks, implemented using bidirectional modified gated recurrent units, with f-divergence serving as the objective function to guide optimization. Compared to existing deep learning-based methods, tf-BiGAIN introduces two key innovations. First, the use of f-divergence provides a flexible and adaptable framework for optimizing the model across diverse imputation tasks, enhancing its versatility. Second, the use of bidirectional gated recurrent units allows the model to leverage both forward and backward temporal information. This bidirectional approach enables the model to effectively capture dependencies from both past and future observations, enhancing its imputation accuracy and robustness. We applied tf-BiGAIN to analyze two real-world time-series datasets, demonstrating its superior performance in imputing missing values and outperforming existing methods in terms of accuracy and robustness. Full article

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30 pages, 6909 KiB

Open AccessArticle

The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing

by Marco Riani, Anthony C. Atkinson, Gianluca Morelli and Aldo Corbellini

Stats 2025, 8(1), 6; https://doi.org/10.3390/stats8010006 - 8 Jan 2025

Abstract

Routine least squares regression analyses may sometimes miss important aspects of data. To exemplify this point we analyse a set of 1171 observations from a questionnaire intended to illuminate the relationship between customer loyalty and perceptions of such factors as price and community [...] Read more.

Routine least squares regression analyses may sometimes miss important aspects of data. To exemplify this point we analyse a set of 1171 observations from a questionnaire intended to illuminate the relationship between customer loyalty and perceptions of such factors as price and community outreach. Our analysis makes much use of graphics and data monitoring to provide a paradigmatic example of the use of modern robust statistical tools based on graphical interaction with data. We start with regression. We perform such an analysis and find significant regression on all factors. However, a variety of plots show that there are some unexplained features, which are not eliminated by response transformation. Accordingly, we turn to robust analyses, intended to give answers unaffected by the presence of data contamination. A robust analysis using a non-parametric model leads to the increased significance of transformations of the explanatory variables. These transformations provide improved insight into consumer behaviour. We provide suggestions for a structured approach to modern robust regression and give links to the software used for our data analyses. Full article

(This article belongs to the Section Regression Models)

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