A Combined Robust Estimator Between the Least Squares Estimator and a t-type Regression Estimator

When the distribution of the errors in linear regression follows a normal distribution the least squares estimator is most efficient. However, if it follows a heavy-tailed distribution such as t distribution, then the least squares estimator is no longer efficient. We propose a combined estimator between the least squares estimator and a t-type regression estimator which is efficient even if the errors have a heavy-tailed or thin-tailed distributions. We calculated the asymptotic property of the proposed estimator. The results of simulation showed that the proposed estimator is robust and effective in many situations.