Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators.

This paper introduces a two-parameters generator of continuous statistical probability distributions called the Alpha Power Rayleigh-G (APRAY-G) family, some statistical properties of the family of distributions were derived, and we introduced a two-submodels of the generator. We estimate the parameters of the models based on the method of maximum likelihood estimation and explored simulation studies based on the introduced submodels. We observed that the biasedness and root mean square errors decrease as the sample size becomes large. We examined the applications of the models based on real-life data sets. We compared the obtained results with some existing probability distribution models. The results showed that the proposed models gave a better fitness to the data under investigation.

Severe multicollinearity can make ordinary least squares estimates unstable by inflating their variances. This paper proposes a KL–James–Stein estimator for ill-conditioned linear regression by combining the Kibria–Lukman transformation with a James–Stein-type shrinkage factor. The bias, covariance, matrix mean squared error, and scalar mean squared error of the estimator are derived and compared with those of existing biased estimators. Monte Carlo simulations are used to examine finite-sample performance under different sample sizes, error variances, and levels of correlation among the regressors. The results show that the proposed estimator often attains smaller scalar mean squared error, especially when collinearity is strong. Two empirical applications, based on the Portland cement and Boston housing datasets, provide further evidence on its practical behavior. Overall, the KL–JSE estimator offers a competitive alternative for ill-conditioned regression problems, although its gains depend on the design structure and the resulting bias–variance trade-off.

This study compared four regularized regression techniques Ridge, Least Absolute Shrinkage and Selection Operator (LASSO), Adaptive LASSO, and Elastic Net to analyze survival models for HIV progression. The HIV patients were those under antiretroviral treatment, considered alongside some demographic and health variables. The selection criteria for the model with the best performance in this study were the Concordance Index (C-index) for ranking ability, Brier Score for predictive accuracy, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Akaike Information Criterion corrected (AICc), and Mean Square Error (MSE). The result showed that for the Ridge model, age, viral load, height, and WHO clinical stage of a patient were associated with lower survival probability (HR > 1) while sex, educational level, marital status, job status, and Body Mass Index of a patent had higher survival probability (HR < 1). LASSO and Elastic Net models showed that the height and WHO clinical stage of a patient were associated with reduced survival while the Adaptive LASSO model indicated that the WHO clinical stage is associated with lower survival probability. The analysis revealed that Adaptive LASSO had the lowest Brier Score, AIC, BIC, AICc, MSE, and highest C-index among the models evaluated when a highly collinear variable was removed. Elastic net had better performance when all predictors were included in the model, indicating that Elastic Net performed better than other models in terms of prediction accuracy and robustness against multicollinearity.