A Variable Selection Procedure for Linear Regression with In uential Observations

Mathematical Subject Classification: 62F07; 62J20 Abstract: Variable selection is very important for statistical modelling. It is also very dicult even for linear regression when the data sets contain in uential observations (IOs). The reason is that the variable selection results often strongly depend on how many and which IOs are included in the data sets, and, on the other hand, the results of IO detection also strongly depend on how many and which variables are included in the model. In this paper, a procedure based on backward elimination (BE) is proposed. Firstly, a three-step-one-case (TSOC) procedure of IO detection for a given model is proposed. Then, in every cycle of BE the F-test for each pair of hypotheses Hj: j = 0 and Kj: j 6 = 0 is performed using data set not including all the IOs, detected by TSOC, of the two models under Hj and Kj respectively. The simulation results and an example show that the proposed procedure performs bette