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The violation of the assumptions of no multicollinearity among predictors and homoscedasticity poses a very challenging situation in regression analysis. This situation leads to inflated variance and makes the inference of the coefficient insignificant. The ridge estimators generally involve the error variance obtained using the ordinary least square approach under homoscedasticity. In this study, we have designed a novel idea to use a heteroscedasticity consistent estimator when a joint issue of multicollinearity and heteroscedasticity is present in the data. This suggestion is simple and effective in improving the performance of the ridge estimators. The proposed suggestion of heteroscedastic error variance is implemented on seven popular ridge estimators in the study. However, this can be utilized for any ridge estimator that is a function of error variance. The performance of the new estimators is explored using an extensive simulation study in terms of mean squared error (MSE). The results demonstrate that the proposed estimators consistently yield lower MSE values compared to their classical counterparts, particularly in the presence of both multicollinearity and heteroscedasticity. The heteroscedastic error variance adjustment plays a pivotal role in achieving these improvements. The use of proposed estimators has also been illustrated using real-life applications.
Dar et al. (Wed,) studied this question.