Stats

18 pages, 339 KiB

Open AccessArticle

Estimation of Weighted Extropy Under the α-Mixing Dependence Condition

by Radhakumari Maya, Archana Krishnakumar, Muhammed Rasheed Irshad and Christophe Chesneau

Stats 2025, 8(2), 34; https://doi.org/10.3390/stats8020034 - 1 May 2025

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Introduced as a complementary concept to Shannon entropy, extropy provides an alternative perspective for measuring uncertainty. While useful in areas such as reliability theory and scoring rules, extropy in its original form treats all outcomes equally, which can limit its applicability in real-world [...] Read more.

Introduced as a complementary concept to Shannon entropy, extropy provides an alternative perspective for measuring uncertainty. While useful in areas such as reliability theory and scoring rules, extropy in its original form treats all outcomes equally, which can limit its applicability in real-world settings where different outcomes have varying degrees of importance. To address this, the weighted extropy measure incorporates a weight function that reflects the relative significance of outcomes, thereby increasing the flexibility and sensitivity of uncertainty quantification. In this paper, we propose a novel recursive non-parametric kernel estimator for weighted extropy based on

α

-mixing dependent observations, a common setting in time series and stochastic processes. The recursive formulation allows for efficient updating with sequential data, making it particularly suitable for real-time analysis. We establish several theoretical properties of the estimator, including its recursive structure, consistency, and asymptotic behavior under mild regularity conditions. A comprehensive simulation study and data application demonstrate the practical performance of the estimator and validate its superiority over the non-recursive kernel estimator in terms of accuracy and computational efficiency. The results confirm the relevance of the method for dynamic, dependent, and weighted systems. Full article

17 pages, 646 KiB

Open AccessArticle

A Smoothed Three-Part Redescending M-Estimator

by Alistair J. Martin and Brenton R. Clarke

Stats 2025, 8(2), 33; https://doi.org/10.3390/stats8020033 - 30 Apr 2025

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Abstract

A smoothed M-estimator is derived from Hampel’s three-part redescending estimator for location and scale. The estimator is shown to be weakly continuous and Fréchet differentiable in the neighbourhood of the normal distribution. Asymptotic assessment is conducted at asymmetric contaminating distributions, where smoothing is [...] Read more.

A smoothed M-estimator is derived from Hampel’s three-part redescending estimator for location and scale. The estimator is shown to be weakly continuous and Fréchet differentiable in the neighbourhood of the normal distribution. Asymptotic assessment is conducted at asymmetric contaminating distributions, where smoothing is shown to improve variance and change-of-variance sensitivity. Other robust metrics compared are largely unchanged, and therefore, the smoothed functions represent an improvement for asymmetric contamination near the rejection point with little downside. Full article

(This article belongs to the Section Statistical Methods)

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16 pages, 534 KiB

Open AccessArticle

Longitudinal Survival Analysis Using First Hitting Time Threshold Regression: With Applications to Wiener Processes

by Ya-Shan Cheng, Yiming Chen and Mei-Ling Ting Lee

Stats 2025, 8(2), 32; https://doi.org/10.3390/stats8020032 - 28 Apr 2025

Viewed by 135

Abstract

First-hitting time threshold regression (TR) is well-known for analyzing event time data without the proportional hazards assumption. To date, most applications and software are developed for cross-sectional data. In this paper, using the Markov property of processes with stationary independent increments, we present [...] Read more.

First-hitting time threshold regression (TR) is well-known for analyzing event time data without the proportional hazards assumption. To date, most applications and software are developed for cross-sectional data. In this paper, using the Markov property of processes with stationary independent increments, we present methods and procedures for conducting longitudinal threshold regression (LTR) for event time data with or without covariates. We demonstrate the usage of LTR in two case scenarios, namely, analyzing laser reliability data without covariates, and cardiovascular health data with time-dependent covariates. Moreover, we provide a simple-to-use R function for LTR estimation for applications using Wiener processes. Full article

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34 pages, 353 KiB

Open AccessArticle

Adaptive Clinical Trials and Sample Size Determination in the Presence of Measurement Error and Heterogeneity

by Hassan Farooq, Sajid Ali, Ismail Shah, Ibrahim A. Nafisah and Mohammed M. A. Almazah

Stats 2025, 8(2), 31; https://doi.org/10.3390/stats8020031 - 25 Apr 2025

Viewed by 106

Abstract

Adaptive clinical trials offer a flexible approach for refining sample sizes during ongoing research to enhance their efficiency. This study delves into improving sample size recalculation through resampling techniques, employing measurement error and mixed distribution models. The research employs diverse sample size-recalculation strategies [...] Read more.

Adaptive clinical trials offer a flexible approach for refining sample sizes during ongoing research to enhance their efficiency. This study delves into improving sample size recalculation through resampling techniques, employing measurement error and mixed distribution models. The research employs diverse sample size-recalculation strategies standard simulation, R1 and R2 approaches where R1 considers the mean and R2 employs both mean and standard deviation as summary locations. These strategies are tested against observed conditional power (OCP), restricted observed conditional power (ROCP), promising zone (PZ) and group sequential design (GSD). The key findings indicate that the R1 approach, capitalizing on mean as a summary location, outperforms standard recalculations without resampling as it mitigates variability in recalculated sample sizes across effect sizes. The OCP exhibits superior performance within the R1 approach compared to ROCP, PZ and GSD due to enhanced conditional power. However, a tendency to inflate the initial stage’s sample size is observed in the R1 approach, prompting the development of the R2 approach that considers mean and standard deviation. The ROCP in the R2 approach demonstrates robust performance across most effect sizes, although GSD retains superiority within the R2 approach due to its sample size boundary. Notably, sample size-recalculation designs perform worse than R1 for specific effect sizes, attributed to inefficiencies in approaching target sample sizes. The resampling-based approaches, particularly R1 and R2, offer improved sample size recalculation over conventional methods. The R1 approach excels in minimizing recalculated sample size variability, while the R2 approach presents a refined alternative. Full article

25 pages, 6923 KiB

Open AccessCommunication

An Integrated Hybrid-Stochastic Framework for Agro-Meteorological Prediction Under Environmental Uncertainty

by Mohsen Pourmohammad Shahvar, Davide Valenti, Alfonso Collura, Salvatore Micciche, Vittorio Farina and Giovanni Marsella

Stats 2025, 8(2), 30; https://doi.org/10.3390/stats8020030 - 25 Apr 2025

Viewed by 133

Abstract

This study presents a comprehensive framework for agro-meteorological prediction, combining stochastic modeling, machine learning techniques, and environmental feature engineering to address challenges in yield prediction and wind behavior modeling. Focused on mango cultivation in the Mediterranean region, the workflow integrates diverse datasets, including [...] Read more.

This study presents a comprehensive framework for agro-meteorological prediction, combining stochastic modeling, machine learning techniques, and environmental feature engineering to address challenges in yield prediction and wind behavior modeling. Focused on mango cultivation in the Mediterranean region, the workflow integrates diverse datasets, including satellite-derived variables such as NDVI, soil moisture, and land surface temperature (LST), along with meteorological features like wind speed and direction. Stochastic modeling was employed to capture environmental variability, while a proxy yield was defined using key environmental factors in the absence of direct field yield measurements. Machine learning models, including random forest and multi-layer perceptron (MLP), were hybridized to improve the prediction accuracy for both proxy yield and wind components (U and V that represent the east–west and north–south wind movement). The hybrid model achieved mean squared error (MSE) values of 0.333 for U and 0.181 for V, with corresponding R² values of 0.8939 and 0.9339, respectively, outperforming the individual models and demonstrating reliable generalization in the 2022 test set. Additionally, although NDVI is traditionally important in crop monitoring, its low temporal variability across the observation period resulted in minimal contribution to the final prediction, as confirmed by feature importance analysis. Furthermore, the analysis revealed the significant influence of environmental factors such as LST, precipitable water, and soil moisture on yield dynamics, while wind visualization over digital elevation models (DEMs) highlighted the impact of terrain features on the wind patterns. The results demonstrate the effectiveness of combining stochastic and machine learning approaches in agricultural modeling, offering valuable insights for crop management and climate adaptation strategies. Full article

(This article belongs to the Section Applied Statistics and Machine Learning Methods)

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29 pages, 572 KiB

Open AccessArticle

Bias-Corrected Fixed Item Parameter Calibration, with an Application to PISA Data

by Alexander Robitzsch

Stats 2025, 8(2), 29; https://doi.org/10.3390/stats8020029 - 24 Apr 2025

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Abstract

Fixed item parameter calibration (FIPC) is commonly used to compare groups or countries using an item response theory model with a common set of fixed item parameters. However, FIPC has been shown to produce biased estimates of group means and standard deviations in [...] Read more.

Fixed item parameter calibration (FIPC) is commonly used to compare groups or countries using an item response theory model with a common set of fixed item parameters. However, FIPC has been shown to produce biased estimates of group means and standard deviations in the presence of random differential item functioning (DIF). To address this, a bias-corrected variant of FIPC, called BCFIPC, is introduced in this article. BCFIPC eliminated the bias of FIPC with only minor efficiency losses in certain simulation conditions, but substantial precision gains in many others, particularly for estimating group standard deviations. Finally, a comparison of both methods using the PISA 2009 dataset revealed relatively large differences in country means and standard deviations. Full article

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34 pages, 2528 KiB

Open AccessFeature PaperArticle

Inferences About Two-Parameter Multicollinear Gaussian Linear Regression Models: An Empirical Type I Error and Power Comparison

by Md Ariful Hoque, Zoran Bursac and B. M. Golam Kibria

Stats 2025, 8(2), 28; https://doi.org/10.3390/stats8020028 - 23 Apr 2025

Viewed by 197

Abstract

In linear regression analysis, the independence assumption is crucial and the ordinary least square (OLS) estimator generally regarded as the Best Linear Unbiased Estimator (BLUE) is applied. However, multicollinearity can complicate the estimation of the effect of individual variables, leading to potential inaccurate [...] Read more.

In linear regression analysis, the independence assumption is crucial and the ordinary least square (OLS) estimator generally regarded as the Best Linear Unbiased Estimator (BLUE) is applied. However, multicollinearity can complicate the estimation of the effect of individual variables, leading to potential inaccurate statistical inferences. Because of this issue, different types of two-parameter estimators have been explored. This paper compares t-tests for assessing the significance of regression coefficients, including several two-parameter estimators. We conduct a Monte Carlo study to evaluate these methods by examining their empirical type I error and power characteristics, based on established protocols. The simulation results indicate that some two-parameter estimators achieve better power gains while preserving the nominal size at 5%. Real-life data are analyzed to illustrate the findings of this paper. Full article

(This article belongs to the Section Statistical Methods)

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25 pages, 2840 KiB

Open AccessArticle

Detailed Command vs. Mission Command: A Cancer-Stage Model of Institutional Decision-Making

by Rodrick Wallace

Stats 2025, 8(2), 27; https://doi.org/10.3390/stats8020027 - 19 Apr 2025

Viewed by 158

Abstract

Those accustomed to acting within ‘normal’ bureaucracies will have experienced the degradation, distortion, and stunting imposed by inordinate levels of hierarchical ‘decision structure’, particularly under the critical time constraints so fondly exploited by John Boyd and his followers. Here, via an approach based [...] Read more.

Those accustomed to acting within ‘normal’ bureaucracies will have experienced the degradation, distortion, and stunting imposed by inordinate levels of hierarchical ‘decision structure’, particularly under the critical time constraints so fondly exploited by John Boyd and his followers. Here, via an approach based on the asymptotic limit theorems of information and control theories, we explore this dynamic in detail, abducting ideas from the theory of carcinogenesis. The resulting probability models can, with some effort, be converted into new statistical tools for analysis of real time, real world data involving cognitive phenomena and their dysfunctions across a considerable range of scales and levels of organization. Full article

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38 pages, 844 KiB

Open AccessArticle

The New Marshall–Olkin–Type II Exponentiated Half-Logistic–Odd Burr X-G Family of Distributions with Properties and Applications

by Broderick Oluyede, Thatayaone Moakofi and Gomolemo Lekono

Stats 2025, 8(2), 26; https://doi.org/10.3390/stats8020026 - 4 Apr 2025

Viewed by 209

Abstract

We develop a novel family of distributions named the Marshall–Olkin type II exponentiated half-logistic–odd Burr X-G distribution. Several mathematical properties including linear representation of the density function, Rényi entropy, probability-weighted moments, and distribution of order statistics are obtained. Different estimation methods are employed [...] Read more.

We develop a novel family of distributions named the Marshall–Olkin type II exponentiated half-logistic–odd Burr X-G distribution. Several mathematical properties including linear representation of the density function, Rényi entropy, probability-weighted moments, and distribution of order statistics are obtained. Different estimation methods are employed to estimate the unknown parameters of the new distribution. A simulation study is conducted to assess the effectiveness of the estimation methods. A special model of the new distribution is used to show its usefulness in various disciplines. Full article

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19 pages, 296 KiB

Open AccessArticle

Affine Calculus for Constrained Minima of the Kullback–Leibler Divergence

by Giovanni Pistone

Stats 2025, 8(2), 25; https://doi.org/10.3390/stats8020025 - 21 Mar 2025

Viewed by 160

Abstract

The non-parametric version of Amari’s dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical structure that includes both probability densities and random variables to [...] Read more.

The non-parametric version of Amari’s dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical structure that includes both probability densities and random variables to capture the spirit of Fisherian statistics. We focus on computations involving a constrained minimization of the Kullback–Leibler divergence. We show how to obtain neat and principled versions of known computations in applications such as mean-field approximation, adversarial generative models, and variational Bayes. Full article

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Stats, Volume 8, Issue 2 (June 2025) – 10 articles

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