Sensitivity analysis for predictor variables in the MSAE regression
The minimum sum of absolute errors MSAE regression is more resistant to outliers, than the least squares regression, in the values of the response variable and long-tailed error distributions. Because all observations are used to compute the least squares estimates of the parameters of the model, a small change in the value of the response or the predictor variable will effect the estimates. The MSAE estimates of the unknown parameters are completely determined by a subset of observations; therefore, small changes in some of the values of the response or a predictor variable may not affect the MSAE estimates. The basic idea behind influence analysis is that a regression solution should be stable, that is, small changes in the data should not produce large changes in the results. This is Tukey's property of resistance. At times deleting an observation is one way of introducing small changes in the data. However, this may not be a good way to judge the influence of an observation for the MSAE regression. In this paper, we develop a procedure to find an interval on each value of the predictor variable (leaving all other values undisturbed) that leaves the fitted MSAE regression model unchanged. These intervals show the extent of admissible changes in the values of predictor variables to which the fitted MSAE is resistant. This property may be called complete (or absolute) resistance.
sensitivity analysis influence analysis: l1-norm least absolute value linear programming minimum sum of absolute errors regression robust