This paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just...

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse...

At the present time there is no well accepted test for determining whether or not robust regression parameter estimates are significantly different than least squares estimates. Thus. we propose and demonstrate the efficacy of two Wald-like statistical tests for the above purposes using...