Abstract
Regression depth is one of the data depth which is methods of measuring the generalized multivariate median. Regression depth method is introduced by extending the ideas of location depth (halfspace depth) of Tukey to the regression setting. In this paper, we consider a modified deepest regression estimator (DRE) in simple regression. DRE is defined by taking the average of all candidate fits with largest regression depth. DRE is a robust regression estimator because it has high breakdown point and high asymptotic efficiency. However, in simple regression, the performance of DRE is not high in case of small sample size with outliers. We propose an estimator that takes the median of all candidate fits with maximal regression depth. We investigate the performance of our estimator by simulation studies. Our estimator is compared with the original DRE. The results are that mean squared error of our DRE is smaller than that of other estimators using regression depth in small and large sample size with outliers.
