MODIFIED FUZZY-ROBUST RIDGE REGRESSION FOR MULTICOLLINEAR, OUTLIER-CONTAMINATED DATA
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Multicollinearity, Outliers, Ridge Regression, Robust regression, Fuzzy robust regression
Abstract
Multicollinearity is known to have a significant impact on the stability of linear regression parameter estimation, while the presence of outliers tends to compound this problem. Ridge regression helps to improve the multicollinearity problem, but it is highly sensitive to outliers. This paper proposes Modified Fuzzy Robust Ridge Regression (MFRRR), which modifies classical ridge regression by adapting the penalty parameter through modified fuzzy robust estimators based on weighted residual membership functions. The method is evaluated under challenging data conditions involving simultaneous multicollinearity, outliers, and fuzzy uncertainty. Performance is assessed using both a real body fat dataset and Monte Carlo simulations with varying sample sizes correlation levels and contamination rates . MFRRR is compared to ordinary least squares (OLS), ridge regression, and robust ridge regression based on the mean absolute error (MAE) as an evaluation criterion. These findings indicate that MFRRR is always associated with smaller prediction errors and more reliable parameter estimates, especially when there is high multicollinearity and data contamination
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