A heuristic approach to combat multicollinearity in least trimmed squares regression analysis

In order to down-weight or ignore unusual data and multicollinearity effects, some alternative robust estimators are introduced. Firstly, a ridge least trimmed squares approach is discussed. Then, based on a penalization scheme, a nonlinear integer programming problem is suggested. Because of complexity and difficulty, the proposed optimization problem is solved by a tabu search heuristic algorithm. Also, the robust generalized cross validation criterion is employed for selecting the optimal ridge parameter. Finally, a simulation case and two real-world data sets are computationally studied to support our theoretical discussions.