The researchers developed a new method called Ridge Least Median Squares (RLMS) to estimate parameters in multiple linear regression when dealing with multicollinearity and outliers. They compared RLMS with other methods like Ordinary Least Squares (OLS) and found that RLMS performed better in handling these issues. The results from simulations and real-life data showed that RLMS is more effective in reducing errors caused by multicollinearity and outliers.