The Rank-based Robust Regression Analysis And Diagnosis Method

The Regression analysis is employed extensively in clinical and medical research. However in many cases the data derived from trials and (or) experiments are away from the supposed model or unsuitable to the supposed assumptions, thus the ordinary LS (least squares) regression will be influenced enormously and even result in the unexplained results. Robust regression is a good alternative when we encounter these questions in medical studies. Based on the preceding achievement of robust regression study the author introduce a new kind of rank-based robust regression, discuss regression diagnosis and offer some medical examples to verify the methods.In 1972 Jackel introduced rank-based regression analysis (R estimator) which can decrease the influence of outliers in Y space on the regression estimator by means of introducing the function of residual rank into the model as weight function. The estimator is available when the error distributions are dissatisfied with normality. When the supposed model is inappropriate the estimator is immune to it. And an advantage of the rank-based methods is that they have excellent efficiency properties over a wide class of error distributions including asymmetric distributions. However there are X-outliers, R estimator can abate. We can generalize the score function to the function of the distance between the case and the center of the all points, and get GRestimator in order to avoid the effect of X-outliers. But the breakdown of the estimator is not high. Be similar to the idea of GR, we can achieve the HBR (high breakdown) estimator which have higher breakdown than GR estimator by means of enlarging the function into the two-dimension space of X and Y. The Breakdown of HBR will get 50% and increase the robustness. In this study we discuss the robust quality and relative efficiency and think about their regression diagnosis. When the error distribution is normal, R and GR estimator have relatively high efficiency and even get 95%, while the HBR efficiency is bad. The higher breakdown the estimator is, the lower the efficiency is. As far as regression diagnosis is concerned, R estimator can identify outliers and test the fitness of supposed model. The model fitness test of GR and HBR estimator is not good. However they can effectively identify suspicious point.The proceedings of the kind of estimators and statistical diagnosis are achieved by means of SAS/IML.