TELBS robust linear regression method

MA Tabatabai,1 WM Eby,1 H Li,1 S Bae,2 KP Singh21Department of Mathematical Sciences, Cameron University, Lawton, OK, 2Department of Medicine, University of Alabama, Birmingham, AL, USAAbstract: Ordinary least squares estimates can behave badly when outliers are present. An alternative is to use a robust regression technique that can handle outliers and influential observations. We introduce a new robust estimation method called TELBS robust regression method. We also introduce a new measurement called Sh(i) for detecting influential observations. In addition, a new measure for goodness of fit, called R2RFPR, is introduced. We provide an algorithm to perform the TELBS estimation of regression parameters. Real and simulated data sets are used to assess the performance of this new estimator. In simulated data with outliers, the TELBS estimator of regression parameters performs better in comparison with least squares, M and MM estimators, with respect to both bias and mean squared error. For rat liver weights data, none of the estimators (least squares, M, and MM) are able to estimate the parameters accurately. However, TELBS does give an accurate estimate. Using real data for brain imaging, the TELBS and MM methods were equally accurate. In both of these real data sets, the Sh(i) measure was very effective in identifying influential observations. The robustness and simplicity of computations of TELBS model parameters make this method an appropriate one for analysis of linear regression. Algorithms and programs have been provided for ease in implementation, including all relevant statistics necessary to perform a complete analysis of linear regression.Keywords: robust linear regression, least squares estimator, M and MM estimators, magnetic resonance imaging, Cook's distance, detection of influential observations, Studentized residual