New method beats traditional estimators for accurate linear regression in outliers.
A new method called quantile based ridge M-estimator was developed to improve estimates in linear regression models with multicollinearity and outliers. This method automatically adjusts the ridge parameter based on the level of noise and multicollinearity in the data. The new estimator outperformed traditional methods like ordinary least squares and ridge estimators, especially when there is high multicollinearity, significant error variance, and outliers in the data. It also works well with different types of error distributions, not just normal distribution. Two real-life examples were used to show how this new method can be applied effectively.