International Journal of Statistics and Probability, Issue: Vol.15, No.1

Assessment of Traditional and Community Mathematical Knowledge About the Concept of Volume in Both Indigenous and General Primary Schools in Hidalgo

Tue, 31 Mar 2026 14:05:46 +0000

This study analyzes community and ancestral mathematical knowledge about volume among students in Indigenous and general primary schools in the state of Hidalgo, Mexico. The objective was to estimate the expected probability of presence of this knowledge (Y₂), considering contextual demographic and cultural factors. Eleven explanatory variables were considered (age, sex, community, municipality, economic community activities, parents and grandparents, parents' and grandparents' education, and school activities), and several counting models were adjusted and compared (Poisson, quasi-Poisson, and negative binomial). Finally, a negative binomial regression model with a log link function was selected. Parameters were estimated using maximum likelihood (Fisher-Scoring), and fit was assessed using deviance, AIC, and the D/df ratio.

Only three predictors were statistically significant: age (β₁=-0.09, p=0.07), community (β₂=-0.61, p<0.001), and school activities (β₃=+0.33, p<0.001). The adjusted deviation of 0.10006 and the lowest AIC (1299.9) indicates a good fit. When transforming the predictions to the original scale, no combination of variables sufficiently raises Y₂ to be considered representative of the presence of knowledge in the communities studied. Although variables such as community and school activities had a significant influence, their practical impact is limited. Whereas the negative binomial model proved to be adequate for explaining the relationship between demographic and contextual variables and volume of knowledge, the coefficients suggest that these factors do not impact the practical representativeness of knowledge.

Comparative Performance of Machine Learning Models for Diabetes Prediction Among US Adults Using NHANES Data

Wed, 25 Mar 2026 16:36:43 +0000

This study aimed to compare the performance of six popular machine learning (ML) models for predicting diabetes mellitus among US adults using data from the 2017-March 2020 cycle of the National Health and Nutrition Examination Survey (NHANES). Data from 6,170 NHANES participants aged 20 years and older were analyzed. The target variable was self-reported diabetes status. A comprehensive set of predictors spanning demographics, health behaviors, and body measurements was considered. Descriptive statistics, accounting for NHANES’s complex sampling design, were presented to characterize the study population. To train the ML models, data were preprocessed using min-max normalization and the Synthetic Minority Oversampling Technique (SMOTE) to address class imbalance. Six ML models —logistic regression (LR), k-Nearest neighbors (kNN), support vector machine (SVM), random forest (RF), extreme gradient boosting (XGBoost), and neural networks (NN) —were trained and optimized using grid search and 10-fold cross-validation. Model performance was evaluated using sensitivity, specificity, accuracy, and AUC. Statistical differences in performance matrices were tested using Cochran’s Q and pairwise McNemar’s tests. Regarding models’ predictive ability, the RF model achieved the highest AUC (0.7559) and sensitivity (0.5370), while XGBoost showed the highest specificity (0.8654) and accuracy (0.7909). The NN model had consistent performance (AUC: 0.7482 ± 0.0054; sensitivity: 0.4828 ± 0.0493). A Cochran’s Q test indicated significant differences in all metrics (sensitivity, specificity, accuracy and AUC) across models (p-value < 0.001). Pairwise McNemar’s tests further confirmed multiple statistically significant differences in metrics within some models.

A Boundary Bias Robust Estimator for Finite Population Total

Tue, 31 Mar 2026 14:13:26 +0000

This paper addresses the persistent problem of boundary bias in kernel-assisted finite population estimation under simple random sampling without replacement. We propose an Adaptive Boosting (AdaBoost) enhanced Nadaraya-Watson estimator that iteratively reweights observations to reduce boundary bias. The method focuses learning on poorly estimated regions near domain boundaries while maintaining the design-based properties required for finite population inference. Comprehensive simulation studies and real life application across five superpopulation models (Linear, Quadratic, Exponential, Jump, and Sine) demonstrate that the boosted estimator achieves substantial improvements over standard approaches. For moderately varying functions, we observe 11-14% reductions in both bias and root mean squared error (RMSE), with confidence intervals narrowing by 31% on average. The second boosting iteration exhibits superlinear convergence ( α= -1:41), representing a 14.6% acceleration over baseline methods. While e ective for linear and moderately nonlinear functions, the method shows limited utility for highly skewed exponential patterns. These findings offer practitioners a robust tool for boundary bias correction in survey estimation with clear guidelines for application.

Interpreting Distributional Change Beyond the Global Mean Using Standard Error–Defined Central Regions

Mon, 30 Mar 2026 22:51:25 +0000

Global means are routinely used to summarize central tendency and to infer directional change in empirical data. Under distributional change, however, identical shifts in the global mean may arise from fundamentally different structural mechanisms, including asymmetric tail expansion, tail contraction, or redistribution within the central portion of the distribution. This ambiguity limits the interpretability of mean-based inference, particularly in dynamic or non-stationary settings.

This paper examines the relationship between changes in the global mean and changes within a standard error–defined central region, operationally defined as the interval bounded by ±1 standard error around the baseline mean. The mean computed within this region provides a conditional summary of values most tightly supported by sampling precision. Using schematic and numerically constructed examples, we illustrate how the central region may remain stable, shift weakly in the opposite direction to peripheral changes, or move concordantly with the global mean, even when the latter exhibits comparable directional change.

These patterns demonstrate that the direction of the global mean alone does not reliably indicate the structural source of distributional change. By separating global aggregation from behavior within a standard error–defined central region, the proposed perspective clarifies when apparent mean shifts are driven primarily by peripheral extremes rather than by redistribution of typical values. The approach complements classical summary statistics and offers an interpretive framework for longitudinal analysis, policy evaluation, and applied statistical reasoning.

Correction: Testing for the Eigenvector Based on the Multiple Correlation Coefficient

Tue, 31 Mar 2026 04:03:26 +0000

We propose a novel method for testing the hypothesis of an eigenvector based on the exact distribution of the multiple correlation coefficient under a normal population. In particular, we discuss both nonsingular and singular cases, addressing the relationship between sample size and the number of variables. The proposed test has the advantage of being invariant to the ordering of the target eigenvector, focusing only on whether the target vector is an eigenvector. The ordering of the eigenvector is determined by the minimum angle between the target vector and the sample eigenvector. Furthermore, we demonstrated that type I errors is exactly controlled at a particular significance level, and the power under the specified alternative hypothesis can be calculated by the Gauss hypergeometric function in the nonsingular case. Our simulation studies confirm that the empirical distribution of the test statistic is in agreement with theoretical distribution. - This corrects the article ”Testing for the Eigenvector Based on the Multiple Correlation Coefficient”, International Journal of Statistics and Probability, 14(4), 12. https://doi.org/10.5539/ijsp.v14n4p12

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 15, No. 1

Mon, 30 Mar 2026 23:56:20 +0000

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 15, No. 1