Robust regression with high-dimensional data

In many statistical methods, complications arise when the number of dimensions d in a data set is relatively large. Due to overfitting and multicollinearity, linear regression estimates often suffer from numerical instability when the amount of predictors is large. In this research, I compare regularized regression methods that are developed to alleviate the consequences of multicollinearity and overfitting, such as ridge regression and lasso. I combine these methods with an outlier detection algorithm, developed by Rousseeuw & Van den Bossche (2016), that is capable of finding outlying cells and rows in highdimensional data sets, taking correlations between variables into account. With this combination, high-dimensional regression estimates are found that are robust to both rowwise and cellwise outliers.