A hard re-descending hybrid robust regression estimation technique using direct weights

A hybrid approach of M and R estimators using an iterative procedure is proposed to detect outliers and estimation of regression parameters for linear models. We consider the deviation of each residual from its median to measure the likelihood of the corresponding data point to be an outlier. Also, the proposed work develops a reliable algorithm to estimate parameters of regression model that is unaffected by outliers. The significance of the proposed work is a novel hybrid approach of weighing the observations based on the order of residuals and is computationally simpler. Our proposal is illustrated using Monte Carlo simulation and analysed for few empirical benchmark data sets.