| Popis: |
This paper addresses the challenge of multicollinearity in regression models, a condition that inflates the standard errors of coefficients, leading to unreliable estimates and wider confidence intervals. Multicollinearity, characterized by high intercorrelations among independent variables, undermines model accuracy by increasing the variance of the estimated coefficients, making them more sensitive to changes in the data and difficult to interpret. In this paper, we introduce three novel ridge estimators specifically designed to analyze data affected by multicollinearity. These are the Balanced Log Ridge Estimator (BLRE), the Inverse Influence Ridge Estimator (IIRE), and the Adaptive Shrinkage Ridge Estimator (ASRE), all designed to enhance estimation accuracy and stability in the presence of high multicollinearity and noise. Through Monte Carlo simulations and empirical analysis on a highly correlated real dataset, ASRE consistently demonstrates superior performance, achieving the lowest mean squared error compared to existing ridge estimators. The IIRE and BLRE also perform well; however, ASRE proves to be the most robust, especially in extreme scenarios. In contrast, the ordinary least squares estimator performs poorly under these conditions, underscoring the effectiveness of the new estimators. ASRE is recommended for most situations, with IIRE as a reliable alternative, offering significant improvements in handling multicollinearity. |
