Poisson regression models (PRMs) are widely used for analyzing count data, but their accuracy can be affected by outliers and multicollinearity, leading to unreliable parameter estimates. Outliers introduce bias and inefficiency in the estimation, while multicollinearity leads to an inflated variance and thus increases the mean squared error and weakens the coefficient reliability. The Poisson maximum likelihood estimator often performs poorly under these conditions. To address these issues, researchers have proposed biased estimators such as the Poisson ridge regression estimator and the Poisson modified ridge-type estimator. However, these methods do not effectively handle both problems at the same time. In this study, we introduce a new estimator, the robust Poisson James–Stein estimator (PMT-JSE), which incorporates transformed M-estimation to improve parameter estimation when outliers and multicollinearity are present. Theoretical conditions for its superiority are established, and a Monte Carlo simulation is conducted to compare its performance with that of existing robust estimators. The results show that PMT-JSE provides more stable and accurate estimates. In addition, two real-world applications confirm its effectiveness. Based on these findings, we recommend PMT-JSE for practitioners working with PRMs affected by outliers and multicollinearity.

We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.

Binary meta-analysis studies with rare outcomes frequently include zero or a small number of observations in study groups, creating a sparsity issue with the data. The corrections applied to eliminate the impact of the zero cell counts introduce a bias to the meta-analysis results and potentially distort the inferences about the treatment effect and heterogeneity among the studies. The boundaries of interval estimates become highly biased due to the sparsity of the data. This study proposes two Bayesian random-effects meta-analysis models based on the beta-binomial model with an arc-sine-square-root transformation. The performance of the models in estimating the treatment effect and the in-between study variance is assessed with an extensive Monte Carlo simulation study, and a frequently referred meta-analysis dataset is revisited. The models provide accurate estimates of treatment effect and heterogeneity parameters without a continuity correction. They provide well-calibrated, narrow interval estimates with sufficient coverage of true treatment effect and in-between study variance. They are robust against zero cell counts, very low event probabilities, and unbalanced, skewed data distributions. Recommendations are given for the practical use of the proposed models, and the required model scripts are provided to implement the models using R software.

Nowadays, the increasing demands of smart cities require innovative technologies to optimize resource utilization and minimize costs. This research focuses on the construction sector, specifically the production of advanced high-strength steel. We address practical application problems from the iron and steel factory in Annaba, Algeria, known as fuzzy multi-objective linear programming problems. Two methods are applied: a mathematical model and Artificial Neural Networks (ANNs). Results indicate that the ANN approach offers significant time and effort savings.

This study enables the simultaneous estimations of the unknown parameters of two inverted Nadarajah–Haghighi populations. The estimations are conducted using data collected from joint progressively type-II censored samples from the populations of interest. The estimations are based on the assumption that the parameters of the two populations are unknown and unequal. To achieve this, we use classical and Bayesian estimation methods to obtain point and interval estimates for the various unknown parameters. The maximum likelihood and approximate interval estimates are derived from the classical perspective. From the Bayesian perspective, both Bayes estimates and credible intervals are acquired using gamma prior distributions. The Bayes estimates are calculated using squared error loss and by sampling from the posterior distribution through the Markov chain Monte Carlo procedure. All point and interval estimates are validated through a simulation study. In addition, two physical applications are provided to demonstrate the practical significance of the methodologies employed.