Mitigating multicollinearity using adaptive condition-number-driven ridge estimators

In conventional linear regression analysis, the ordinary least squares (OLS) estimation method is commonly used for parameter estimation; however, it is highly sensitive to multicollinearity among predictor variables, which inflates the variance of the estimators and leads to instability in parameter estimates. To address this, ridge regression is often employed, offering improved stability; however, its effectiveness diminishes under conditions of severe multicollinearity. This study proposes two modified condition-adjusted ridge estimators (MCARE1 and MCARE2), which integrate both the condition number and an explicit function of the error variance into the penalty term. The proposed estimators are designed to improve the estimation of regression coefficients in the presence of multicollinearity. These two-parameter estimators dynamically adjust the shrinkage intensity according to the severity of multicollinearity and the noise level in the data, offering improved robustness in ill-conditioned regression scenarios. Monte Carlo simulations across varying multicollinearity levels, sample sizes, and error variances demonstrate that the proposed estimators consistently outperform OLS and existing ridge methods in terms of mean squared error (MSE). This superior performance is further confirmed through consistent results on two real-world datasets.