bayesian estimation of heteroscedastic skew-normal error regression model

In statistics‎, ‎errors are inherent in data and models‎, ‎particularly heteroscedasticity and skew-normal error structures‎. ‎these errors were simultaneously generated and infused into the data‎, ‎leading to uncertainty in parameter estimation‎. ‎the statistician uses statistical knowledge to elicit information and guide decision-making‎. ‎both classical and bayesian restricted stein-rule least squares were compared when the data were contaminated with the aforementioned errors‎. ‎this study proposed an innovative bayesian generalized restricted stein-rule least squares method with heteroscedastic skew-normal errors‎, ‎which was ultimately found to be more efficient compared to non-bayesian restricted stein-rule least square estimators‎. ‎the study observed excellent performance of the bayesian frameworks‎, ‎including the bayes estimate and posterior mean‎, ‎in comparison to the classical restricted stein-rule least squares estimators‎. ‎therefore‎, ‎the study recommends bayesian generalized restricted stein-rule least squares to analysts and researchers who may encounter such errors in their data‎.