Robust second-order least squares estimation for linear regression models

The second-order least-squares estimator (SLSE), which was proposed by Wang (2003), is asymptotically more efficient than the least-squares estimator (LSE) if the third moment of the error distribution is nonzero. However, it is not robust against outliers. In this paper. we propose two robust second-order least-squares estimators (RSLSE) for linear regression models. RSLSE-I and RSLSE-II, where RSLSE-I is robust against X-outliers and RSLSE-II is robust. against X-outliers and Y-outliers. The basic idea is to choose proper weight matrices, which give a zero weight to an outlier. The RSLSEs are asymptotically normally distributed and are highly efficient with high breakdown point.. Moreover, we compare the RSLSEs with the LSE, the SLSE and the robust MM-estimator through simulation studies and real data examples. The results show that they perform very well and are competitive to other robust regression estimators.